This is where all your items are stored. You'll collect many different items throughout the game, some of which you can use anywhere and some of which that are level specific.
To use an item, open up your backpack by pressing Left on the D-Pad, or by using the "Back" button. Go to the item you wish to use and press 'A' to pull it out. You can then use the item by pressing 'Y', or put it back away with 'B'.
Level specific items will only be visible in your backpack when you are in the level that you can use them in.
Other items are usable in all levels and also in camp, such as your smelling salts, cobweb duster, and your trusty piece of bacon.