What is the significance of a 2-stage trigger?

The first stage should be very light, and give an obvious change in resistance as you reach the second stage. The second stage is stiffer to pull, and lets you know if you squeeze much further, the gun will actually shoot. This allows you to better plan the moment you release a bullet/pellet. Most people when they have an object/target sighted in, pull through the first stage and leave the trigger at the threshold of the second stage. When they are very happy with their site picture, perhaps have corrected for windage and elevation, this is the moment they squeeze through the second stage.
 
A two stage trigger has 2 different leverages on the sear release mechanism. The first stage has more leverage, hence the lighter pull weight. In a well tuned trigger you would use this light weight pull to get the sear to the very edge of releasing, where you would then feel the higher resistance of the second stage, due to it having less leverage but more sear release travel per trigger travel. Then pulling the trigger a very small distance beyond that point will drop the sear and fire the weapon. This allows someone to setup a very light trigger with a short crisp break on the second stage, and still have a plenty of sear engagement to prevent misfire when the trigger is at rest. Basically, you can setup a "hair" trigger that isn't sitting on that hair until you want it to be. I wouldn't be comfortable with a very light single stage trigger with what I consider an acceptable amount of creep. I do have a muzzleloader with a very nice single stage trigger, possibly my favorite, but it breaks at two and a half pounds. Maybe I wouldn't like it as much if I took it apart and saw how close it is to firing when at rest. It isn't hard to setup a trigger that is very likely to fire when the gun is bumped. I hope this makes sense. I treat the first stage almost like a safety. I point the gun, take up the first stage, then my final aiming and breath control, then pfff.