Firing order is the order in which your cylinders ignite. For example, in a 4-cylinder engine, the cylinders don't fire 1-2-3-4, in that order. They will fire something like 1-3-4-2. Why? This is to balance both the forces that the engine creates, and to give you a smoother ride. Sometimes firing orders can get screwed up if spark plug wires are removed without taking notes. If this has happened to you, check out the firing order reference
and get yourself out of trouble.