The Dragon Vault is a special structure that allows you to place Dragons inside it for storage, which is useful if you run out of space but do not want to sell your Dragons.
To place a Dragon inside the Dragon Vault, visit the Dragon you want to store in their habitat and tap the "i" icon.
In the next screen, select "More Options" and then the "Move" option and tap on your Dragon Vault building.
Note that the vault must have a free slot in order to store your dragon, and more slots can be purchased with Gold.
Any Dragons that are stored inside the Dragon Vault will not earn Gold as they normally would inside their habitat.