A geostationary orbit is one in which the speed at which a satellite orbits the Earth coincides with the speed that the Earth turns and at the same latitude, specifically zero, the latitude of the equator. This does not mean that the satellite and the Earth are traveling at the same speed, but rather that the satellite is traveling fast enough so that its orbit matches the Earth's rotation. A satellite orbiting in this way, therefore, appears to be hovering in the same spot in the sky and is directly over the same patch of ground at all times.
A geosynchronous orbit is one in which the satellite is synchronized with the Earth's rotation, but the orbit is tilted with respect to the plane of the equator. A satellite in this orbit will wander up and down in latitude, although it will stay over the same line of longitude. Although the terms "geostationary" and "geosynchronous" are sometimes used interchangeably, they are not the same technically; geostationary orbit is a subset of all possible geosynchronous orbits.
The person most widely credited with developing the concept is noted science fiction author Arthur C. Clarke. Others had earlier pointed out that bodies traveling a certain distance above the Earth on the equatorial plane would remain motionless with respect to the Earth's surface. Clarke, however, published an article in 1945's Wireless World that made the leap from the Germans' rocket research to suggest permanent man-made satellites that could serve as communication relays.
Geostationary objects in orbit must be at a certain distance above the Earth to remain in the same position relative to the Earth's surface; any closer or further away, and the object will not remain in the same position. This distance is 22,236 miles (35,786 kilometers) from the surface.
The first geosynchronous satellite was orbited in 1963, and the first geostationary one the following year. Since the only geostationary orbit for the Earth is in a plane with the equator at 22,236 miles (35,786 kilometers), there is only one circle around the world where these conditions occur. This means that geostationary "real estate" is limited. While satellites are in no danger of bumping in to one another yet, they must be spaced around the circle so that their frequencies do not interfere with the functioning of their nearest neighbors.