The Forestry backpacks have four modes. These modes can be toggled by crouching/sneaking and right clicking with the backpack in hand. The four modes are Normal Mode, Locked Mode, Receiving Mode, and Resupply Mode.
Normal Mode will automatically input picked up items as long as they are accepted in the backpack, and there is space for them. Crouch/sneak+Right clicking a chest with this mode enabled will dump all the backpacks contents into the chest.
Locked Mode will not pick up items. Chest interaction is the same as in Normal Mode.
Receiving Mode will act the same as in Normal Mode, except that chest interaction will put allowed items into the backpack, rather than out.
Resupply Mode is the same as Normal Mode in both item pickup and in chest interaction. Though, it will keep corresponding items in your inventory stocked to a full stack as long as possible.