With a single stage trigger you squeeze the trigger until the hammer is released to take a shot. You do not know exactly when the trigger will break releasing the hammer for the shot. There is also some additional overtravel of the trigger after the shot is fired that may throw off sighting a bit for a follow up shot.
With a two stage trigger you have a take up the trigger until a slight resistance is felt, which is the second stage. It takes an additional pound of pressure to overcome the second stage so you will know precisely when the shot will be let off. If you do not take the shot when you release the trigger it will reset itself. It also has an overtravel adjustment to limit trigger travel once it has been fired which helps to keep on target. You can also pull straight through the second stage when rapid firing.