The Shadow Vault is a separate dungeon that is unlocked for every character, even new ones, after defeating the final boss of the main dungeon with just one character on any difficulty.
Shadow Vault, unlike the main dungeon, has an infinite number of floors and is completely randomized. This means that each floor of the dungeon can have a different theme, no two floors are exactly the same, monsters from different areas are mixed, and every monster is scaled to your level.
You can find the Shadow Vault in Torchlight. It is a separate part of the town that is attached to the southeast corner. Next to the entrance you will find two new quest NPCs: Valeria and Gar. These two NPCs and the Ember finding quest giver are the only ones that give quests for the Shadow Vault.