An idea first proposed by Arthur C. Clarke in a science fiction story. There is a distance from the surface of the planet where the speed of a satellite exactly matches the rotation of the earth. Thus, a satellite placed in said orbit will be seen to be in the same place all the time, relative to the earth. This is an extremely valuable feature for a satellite. So valuable that this band of altitude is now very crowded with satellites. Few spots remain.

On Earth, geo-synchronous orbit about the equator is 42,164 km from the center (which is about 35,000 km from the surface.)

In my comm class in college, the professor said that at an International Telecommunications Conference, he heard a representative from Tonga complain about how their territorial rights were being violated because these geo-synchronous satellites were in their air space (albeit about 35 thousand kilometers up.) Essentially the industrial powers' response was (paraphrasing wildly), "Yeah? So whaddya gonna do about it? Knock 'em down with sticks and rocks?"

Geostationary orbit is achieved when a satellite is placed 33,881 km (22,300 miles) above the surface of the Earth in a path that carries it in the plane of the equator. At this distance a satellite takes exactly 24 hours to travel once around the earth and therefore seems to keep pace with a point on the surface over which it is positioned.
Editor's note: It's not "exactly 24 hours" - it's one sidereal day which is equivalent to 23 hours 56 minutes and 4 seconds of mean solar time. But otherwise that's correct.

Note that a geostationary orbit is a special case of a geosynchronous orbit, which shares the same orbital period but may not be fixed over one surface point (for example, it may have an orbital inclination which takes if from one hemisphere to the other.)