Backpacks are used to carry more items in your inventory. A backpack can store up to 27 items. To open a backpack place the backpack on the ground and then right-click it. To equip a backpack in your chestpiece armor slot (you can't wear armor while wearing the backpack), break your backpack while sneaking. To unequip sneak and then right click the ground. Backpacks will drop their contents when they break or the player dies. In multiplayer you can use someones backpack while it is on their back as long as they are near you and facing away from you.
Note: Any color of wool can be used, (changing the color of wool will not change the color of the backpack)