The Global Positioning System (GPS) is a group of 27 Earth-orbiting satellites (24 in operation and three extras in case one fails). When people talk about a "GPS" they usually mean a GPS receiver. The U.S. military developed and implemented this satellite network as a military navigation system, but now lets everyone use the signals.
These 3,500-pound solar-powered satellites circle the globe at about 12,000 miles per hour, making two complete rotations every day. The orbits are arranged so that every time, everywhere on Earth, at least four satellites are "visible" in the sky.
A GPS receiver's job is to locate four or more of these satellites, figure out the distance to each, and use this information to calculate its own location. This operation is based on a simple mathematical principle called triangulation. In a sense it's like giving every square block on the planet a unique address.