The Alchemy Bags are portable version of the Alchemical Chest. When you left-click a block with an Alchemy Bag, a chest GUI opens. It is the same size as the Alchemical Chest, and is completely portable, effectively tripling your inventory.
You can dye the bags and carry all 16 types in your inventory at once, each carrying over a hundred slots. Also, you can put 15 of the bags in 1 bag, taking up 1 space and giving you 1,500 extra spaces. This, along with Ender Chests, allows you to carry immense amounts of items while traveling,
However, to begin with the recipe is quite costly, but once you advance with Equivalent Exchange, it is quite easy to acquire.
One bug to be careful of though is putting the bag in itself, as when you close the menu, you will lose access to all items inside unless you craft another bag of the same colour.