Equip a pickaxe or axe in the primary slot, and torches or another stackable in secondary (shield) slot.
If your inventory and hotbar are full of items, you cannot pick up the item type of whats in the secondary (shield) slot.

Say you're holding 30 torches and there's one on the ground, you can't pick it up until you open the inventory and click a block to make room. Then the torch will be picked up and added to the held stack.