The Bazaar is a building that makes shops spawn. After you unlock the bank and start the game proper, your next dungeon run will turn up a shop that sells a Gate Scroll. Leaving the dungeon with it unlocks the Bazaar. In order to use it, though, you need to upgrade it for 200 gold. After that, it'll give you a quest to buy every item in a dungeon run. If you swing that, it unlocks the level 2 Bazaar. From there, once you've unlocked the level 3 Bank and beaten Hexx Ruins at least once, a special subdungeon will randomly appear that will unlock Ick Swamp and get you a quest to buy every item on Hexx Ruins. After that, you can pay 1200 gold to unlock the level 3 Bazaar.
Lv 2: Shop Scroll - Start the dungeon with a scroll that summons a shop at the location used. Apothecary - Spawns an extra Apothecary in the dungeon.
Lv 3: Elite Items - You are more likely to find Elite Items in the shops. Quest Items - You are more likely to find Quest Items in the shops.