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A geo-stationary orbit is an orbit of an Earth's satellite whose period of rotation is exactly equal to the period of rotation of Earth about it's polar axis (which is 23 hours, 56 minutes and 4.1 seconds) and whose trajectory is aligned with the Earth's equator.
Any satellite in this orbit will appear as if it is always in the same place in the sky when observed from the same point on the Earth. This orbit is at a distance of approximately 35,900 km from the surface of the Earth. Communication satellites are usually placed into this orbit, with several satellites in the same orbit, distributed around to provide world wide coverage for relaying the telecommunication signals.
A geo-stationary orbit is also sometimes called: stationary, or synchronous orbit.
One can also, launch a satellite into a synchronous orbit that is inclined to the Earth's equator. Once in this orbit, the satellite will trace a figure 8 once every 24 hours. The size and the shape of this figure will depend on the inclination angle.
Other more complicated orbits are also possible - especially if one is considering a space vehicle that has it's own propulsion.