The idea is that a single watcher process replaces all background processes that usually are constantly checking for something new on the net. Instant Messaging, weather alerts, stuff like that.
1) Instead of the apps running on your phone, they run on a server somewhere.
2) When they need to alert you, they send a short notification message directly to Apple.
3) Apple then passes it down to your phone's single background notification process, which is waiting for them. You see or hear the short alert, or hopefully notice a badge number change.
4) You open the app, and it goes out directly to its server and asks for details.