The Potions Bag allows you to store and easily use multiple potions in an item that only takes up one slot in your inventory. While you have the Potions Bag selected push Sneak + Right Click to bring up the GUI. In the GUI you will find slots that you can fill with any Potions that you like. The potions are used in a left to right order. Once your Potions Bag is filled and selected simply push and hold the right click button to consume the first potion. Repeat to consume all of the other potions.
These bags are found in dungeon chests with randomized slot counts. The default is three.