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.)