To understand why the bridge is so great for you, we have to start out with the anatomical definition of Extension. This simply means moving away from the fetal position. The opposite would be flexion, or moving towords the fetal position. The deep back muscles are extension muscles. They pull the spine into correct posture by Extenstion. Obviously, the bridge directly hits these muscles exactly as they were designed to do.
It doesn't stop there though. The bridge is an aerobic isometric exercise since it requires the modest tension of the muscles for a moderately long period of time. This also conditions the deep back muscles since they are mostly built out of slow twitch fiber.
The third benefit of the bridge is that it also hits almost every muscle along the superficial back line. This line is responsible for extension of almost all of the posterior muscles. The bridge makes them all work while performing it. This is significant since even the fitness world will admit that exercises that hit multiple muscles are preferable to ones that isolate for all-around health and conditioning.
This is a lot of ground that is covered in only one exercise. This is why the bridge is so highly regarded in the BW world. If you don't know how to do the bridge or you're too weak, I strongly reccomend Matt Furey's Combat Conditioning if you want to learn how to build up to and execute the bridge properly. Nobody has devoted as much time to building the body up to the point of bridging.
Do yourself a favor if you don't have it yet... ORDER IT NOW!