If you really, really want to know how it really works check out <A HREF="http://www.colorado.edu/geography/gcraft/notes/gps/gps_f.html" TARGET="_blank">www.colorado.edu/geography/gcraft/notes/gps/gps_f.html</A> for a modular discussion of GPS, time and charting at as much of a level of detail as you care to take in.
The Wide Area Augmentation System in the US (still under test, not commissionable until they can prove 99.9999999 availability of accurate signals, which will take a few years) is a differential system that measures inaccuracies in GPS generated positions and provides those corrections over a wide area (Western Hemisphere) via satellite broadcast.
The "competing" system is GLONAS operated by the Russians, a satellite based but incompatible system.
Why Europeans have not taken to GPS, a few guesses:
1. they really have operationally, but can't make a big deal out of it for political reasons
2. not invented here
3. controlled by a foreign military agency
There was/is an animal called European GPS Navigation Overlay System (EGNOS) that would be an augmentation to at least GPS and possibly GLONAS designed to provide improved accuracy in Europe.