Hyrule Castle Underground is a location from The Legend of Zelda: Breath of the Wild. It is an underground area located inside Hyrule Castle in the Hyrule Field region of Central Hyrule.
The Hyrule Castle Underground is made up by four separate areas located under the castle that are considered part of the Castle's dungeon map which includes the Docks, Lockup, East Passage, and West Passage. Its name comes from the Stone Talus (Rare) fought in the East Passage and the Stalnox imprisoned within the Lockup that guards the Hylian Shield as it listed above the mini-bosses' names and boss health bars. The name does not appear on the Sheikah Slate's map when outside the castle (as the 3 dimensional dungeon map appears when Link is inside the castle).
All four areas of the Underground are connected to above ground parts of the castle. The Docks also contain the Saas Ko'sah Shrine which acts as a warp point once its Travel Gate is active. The Passages feature mine cart tracks. The Docks and East Passage are connected to the Library.
Theory[]
Theory warning: This section contains theoretical information based on the research of one or several other users. It has not been officially verified by Nintendo and its factual accuracy is disputed.
Secret Royal Family Escape Routes?[]
Given how the underground and Hyrule Castle are conveniently connected by hidden passages, it is possible they were secret routes used by the Royal Family, their Royal Guards, and/or Sheikah allies to exit and/or enter the castle covertly. This is supported by the docks which would allow escape by way of the moat and would grant their Zora allies easy access into the castle as well as allow the Sheikah to use it as a secret supply route provided the docks existence was a secret known to only the Royal Family and its closest allies. The Library is known to be connected to two areas of the underground and would be easily accessible to the King and Zelda as Rhoam had a secret study and Zelda enjoyed scholarly research so she probably visited the library often to do research in the Library's archives thus these passages may have been likely known to them and existed in case of emergencies or should Hyrule Castle fall under the control of evil forces as had occured many times throughout the kingdom's history. Additionally they could also allow entry into the castle as shown by Link thus could be used to enter the castle to retake it and/or confront the evil forces controlling it. Presumably elite Royal Guards such as Link were aware of these routes to better protect the Royal Family during such emergencies as lesser monsters such as Keese are know to take up residence in underground areas thus they could ensure these minor but still dangerous vermin could be dealt with.
Alternatively the Royal Family could use them to exit the castle covertly and disguise themselves using alter-egos to mingle with the generally population without them knowing. This may have been how King Rhoam learned of the gossip surrounding his daughter as he is known to be a skilled actor and may have used his Old Man alter-ego or another disguise to learn his people's honest opinions and fears concerning the Royal Family. This would allow the Royal Family to better understand the common people and what they might be thinking.
Theory warning: Theories end here.