The Vault, more precisely Odin's Vault, also known as Odin's Treasure Room or the Weapon's Vault, was a room in the Royal Palace of Asgard, which held a number of relics that Odin had gained as a result of his victories over the course of his life.
Odin captured, stole, purchased and did whatever he could to take all the relics and weapons that could bring about Ragnarok (the Asgardian end of times), and he locked them away in a vault in the base of his palace, so anything he thought could bring the universe down is now under lock and key.
Home to the incredibly powerful Casket of Ancient Winters, the Weapon's Vault has always been a prime target for those seeking powerful weapons of destruction. During Thor's crowning ceremony, the Vault is attacked by three Frost Giants attempting to steal the casket. However Odin sensed the Frost Giants in the Vault and activated the Vault's deadliest automaton device the Destroyer to dispatch the the Frost Giants.
The Tesseract was placed in the vault following the Battle of New York. During the Second Dark Elf Conflict, Odin commanded the Einherjar to protect the Weapons' Vault. In the end after the Dark Elves were defeated, their weapon, the Aether, was taken by the Asgardians. However, Sif and Volstagg decided to take it to the Collector for safekeeping, since it was considered unwise to keep two Infinity Stones so close together.