Spoiler warning: Plot or ending details follow.
Guidance Stones are items from The Legend of Zelda: Breath of the Wild. There are several Guidance Stones found within certain Shrines, in every last Sheikah Towers, the Hateno Ancient Tech Lab, and the four Divine Beasts. They have varying functions depending on where they are located, and they all require the Sheikah Slate to function.
Functions[]
The first Guidance Stone Link encounters is found in the Slumber of Restoration chamber where Link awakens. Accessing this Guidance Stone will reward Link with the Sheikah Slate and open the chamber's door allowing Link to venture further into the Shrine of Resurrection. In order to leave the Shrine of Resurrection Link must activate a second Guidance Stone, which opens the door that allows Link to go outside to the Great Plateau. During "Follow the Sheikah Slate", Link is directed by Princess Zelda telepathically to follow his Sheikah Slate, which leads him to another Guidance Stone. This Guidance Stone turns out to be the Guidance Stone for the buried Great Plateau Tower which ends up activating the tower, causing it and other towers to raise from the ground all over Hyrule and causes the Shrines to activate as well, though they remained locked and some remained buried or concealed.
The Guidance Stones within the four Shrines of the Great Plateau region are used to give Link access to the Remote Bomb, Magnesis, Stasis and Cryonis Runes. Accessing any one of these Guidance Stones and obtaining its rune will also allow Link to activate the amiibo Rune functionality which adds the amiibo Rune to the Sheikah Slate.
Within the Sheikah Towers, their purpose is to unveil each regional map of Hyrule with data on the Sheikah Slate. Once the Guidance Stone is used and the tower is activated, Link can warp back to the tower at a moment's notice. If Link can activate a second Tower, the Sheikah Slate's basic rune the Sheikah Sensor will be unlocked allowing him to search for Shrines. Using a tower or shrine's Guidance Stone will activate and add its Travel Gate to the Sheikah Slate allowing Link to use them as warp points.
Within the Hateno Ancient Tech Lab, Purah happens to own a Guidance Stone herself. However, when Link first arrives to the Lab, it is shown that the Guidance Stone is inert as the blue fire that gives it power has gone out. Link must then search for the Ancient Furnace to acquire the blue flame using a torch, then must take the flame uphill while lighting the lanterns along the way to serve as a checkpoint in case his Torch goes out and finally, reignite the stove that fuels the Lab's Guidance Stone so that Link can obtain the Camera Rune, Hyrule Compendium, as well as restore photos taken by Zelda that that have a role in helping the restoration of Link's memories.
After taking a snapshot of Purah, she will then allow Link to upgrade two Runes and the Sheikah Sensor in exchange for some Ancient materials, these being three Ancient Cores for the Stasis Rune, three Ancient Shafts for the Remote Bombs, and finally three Ancient Screws to upgrade the Sheikah Sensor.
Purah and Robbie are shown to care for and dote on their Guidance Stones, becoming happy once Link restores power to them. All normal Guidance Stones are capable of rudimentary speech, though are generally depicted functioning more akin to a computer with a speech function. Purah reveals the Guidance Stone in her lab was originally from Hyrule Castle though it was removed to safety during the Great Calamity. Robbie's was apparently originally part of the Royal Ancient Tech Lab but was removed during the destruction of that tech lab. Purah and Robbie choose their respective labs locations as they were close to deposits of Ancient energy collected by Ancient Furnaces an converted into Blue Flame which they use as free energy to light their lab's Furnaces to power their Guidance Stones.
If Link reads Purah's Diary, Purah will act as if she is angry about him reading it and pretends to use her Guidance Stone to erase all for the data and Runes stored on Link's Sheikah Slate, only to reveal it was a trick and that she had imitated her Guidance Stone's voice to make Link believe she had erased his Sheikah Slate's data (which Purah would not dare do anyways as Link needs the Sheikah Slate to regain his memories and complete his quest). While doing a diagnostic on the Guidance Stone, Purah's assistant Symin finds picture data for the Hyrule Compendium stored on Purah's Guidance Stone and reveals it can be uploaded to fill in missing entries. Purah allows Link and Symin test the upload process out of intellectual curiosity despite noting she hates letting people use it for free (Link first use was payment for relighting the Furnace and the Rune upgrades each cost him Ancient Materials thus neither were truly free). The process uploads a random picture filling in an empty entry. Afterwards Purah notes next time won't be free justifying he pay as it costs money to run her lab and forces Symin to charge him to upload pictures with the price being determined by the type of picture though beyond its type the picture received is random.
It is later revealed that the Sheikah Slate was designed to be used by the Hero Chosen by the Master Sword, thus explaining why Princess Zelda was unable to use the Sheikah Slate to access the Shrines, while the Towers remained buried under the ground. Princess Zelda and her Sheikah allies only realized this after the Great Calamity, thus explaining why Zelda did not have Link use the Sheikah Slate to activate them 100 years earlier. It is implied that had he been able to activate them with the Sheikah Slate, he would have been better prepared for the challenges he faced during the Great Calamity. However one of Link's Recovered Memories shows Princess Zelda attempting to activate the Tena Ko'sah Shrine at the Ancient Columns in Tabantha Frontier though unfortunately it has no power, though Zelda notes to herself that the Shrine was designed only to be accessed by the Hero Chosen by the Master Sword whom she already knows is Link as he is the current chosen bearer of the sword. However Zelda believes designs can be worked around or at least she hopes. Suddenly Link rides up on his horse and Zelda confronts her Royal Knight telling him to return to her father and tell him she is fine and that she doesn't need an escort. However Zelda reveals her resentment towards Link when she yells at him to stop following her in frustration. This suggests Zelda's resentment prevented her from seeking Link's help despite understanding the Shrines were design to be accessed by him. Though she later befriended Link after he saved her from the Yiga Clan even apologizing for her early behavior she nor Purah enlisted his aid though by that time the Great Calamity was drawing near and Zelda was forced to end her research after King Rhoam forbid her to force her to focus on her training to awakening her sealing powers due to being under the impression Zelda was neglecting her duties as Princess to "play scholar" when she was doing everything she could to awaken them even pleading to the gods at the Spring of Power to tell her what it was that was wrong with her while Link stood guard nearby. Though Zelda managed to do a secret survey of the Shrines with the aid of her Sheikah court poet, Link apparently did not accompany them. Purah also explains that at the time the Shrines save for the Shrine of Resurrection had no power as the Sheikah Towers that supplied power to them were still buried and the Great Plateau Tower's Guidance Stone was only revealed as a result of the Great Calamity and Link had already been injured by that point thus was in no condition to activate it with the Sheikah Slate as apparently Zelda, Purah, or Robbie could not do so. Purah later admits she and Zelda didn't understand the basics of how the Shrine, Towers, Guidance Stone, Sheikah Slate, and Link's role were all related though Zelda at least understood the Shrines were designed to be activated by the Chosen Hero though was apparently unwilling (initially) and unable (after befriending him) to enlist Link's aid and even if they had they needed to activate one of the buried towers which would have required excavation and presumably approval from her father. This may explain why King Rhoam watched over Link as Zelda's research team uncovered the Shrine of Resurrection and realizing the ancient medical facility's importance had the Sheikah get it running again which ultimately saved Link's life and had Zelda been permitted to research may have discovered how to restore power to them. King Rhoam did have a change of heart before his death but by that time it was too late. Thus it is implied King Rhoam felt responsible for Zelda's inability to solve the mystery of the Shrines and after his death ensured Link would discover their purpose presumably to make up for his mistakes as a father and King.
It is strongly implied that the Guidance Stones, Sheikah Slate, Sheikah Towers, and Shrines where all created by the ancient Sheikah (which presumably includes the Sheikah Monks) to aid the hero in his quest to defeat Calamity Ganon when he eventually returned.
The Ancient Oven[]
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The Ancient Oven Cherry
In addition to normal Guidance Stones, during the Age of Burning Fields the Sheikah technology researcher Robbie modified his Guidance Stone at the Akkala Ancient Tech Lab to create the Ancient Oven Cherry which could convert guardian parts into ancient soldier gear. Later on, Robbie attempted to modify Cherry even further though his plans where too complex to implement and decided to put them on hold. However his wife Jerrin who had originally been sent by Impa to aid Robbie in his research, managed to complete Robbie's planned upgrades, allowing Cherry to speak like a living person. However Jerrin eventually became jealous of Robbie's interactions with Cherry as he came to rely on it more and more, which Robbie attributed to jealousy towards Cherry's namesake as he had named the Ancient Oven after his first love. After learning of his wife's feelings, Robbie chose to restore Cherry back to her original mechanical way of speaking and avoided referred to her as Cherry in order to avoid upsetting his wife, due to Jerrin's habit of throwing things whenever she heard her husband refer to the Ancient Oven as Cherry. Due in part to his old age, Robbie occasionally slip up and accidentally refer to the Ancient Oven as Cherry as shown when he reunites with Link one hundred years after the Great Calamity, though apparently Jerrin fails to hear him say it as it does not cause an outburst from her when he says it, though it is possible that Jerrin did hear her husband say it and simply keeps her emotions in check and lets it slide while in the presence of company as she may not wish to cause a scene in front of a guest like Link.
Eventually the blue flame Furnace that powered Cherry went out and Robbie was unable to relight it before Link's arrival as his old age prevented him from doing so and he couldn't ask his son Granté to do it as he had left to explore the world and Jerrin refused to relight it due to her dislike of Cherry. After proving his identity to Robbie, he is asked to relight the furnace that powers Cherry so she can make Link ancient soldier gear. Like with Purah's guidance stone, Link must relight the furnace with Blue Flame which he can obtain from the Ancient Furnace at Tumlea Heights in Deep Akkala. After restoring power to Cherry, Link can use her to forge ancient soldier gear in exchange for Rupees and Guardian Parts. Robbie requires Link to pay as due to Robbie lack of funding for his research as the Royal Family of Hyrule had originally funded both Robbie and Purah's research 100 years ago, funding which ended as a result of the Great Calamity thus Robbie compensates by using Cherry's ability to forge Ancient Soldier Gear as a means to generate revenue which he can use to fund his research.
Link can also relight the flame after receiving the 'Robbie's Research" Side Quest from Purah before he even enters the Akkala Ancient Tech Lab and speaking to Robbie. This will restore power to Cherry allowing Link to use her to forge Ancient Soldier Gear without speaking to Robbie or completing the side quest (as it is only completed once Link talks to Robbie after restoring power to Cherry). Additionally Robbie will not require Link to prove his identity if he speaks to Robbie after he relights the flame.
Cherry herself is quite similar to a Gossip Stone albeit more robotic and is similar to the Moonlight Merchant a Gossip Stone merchant from Skyward Sword. This may be intentional as Robbie being a researcher of Sheikah technology may be aware of the existence of Gossip Stones in the past. Though Guidance Stones function as terminals and databases they apparently possess some rudimentary artificial intelligence and speech with Cherry presumably being the most advanced though she does have a minor glitch in her speech after Robbie reverted her back to her robotic manner of speaking. However the Guidance Stones role as database resembles the Gossip Stones role as a source of information indicating the technology may have been an evolution of Gossip Stone concept with Cherry being closest to the Gossip Stones of old as she has personality and intelligence.
Spoiler warning: Spoilers end here.