Geass is the ability to make anyone obey your will. The power rests in the eye of its user, by looking someone in the eye the user of Geass can control someone command someone absolutely. Geass can be used for commands ranging from the mundane (such as finding out the answer to a test) to the extraordinary (suicide).
The known limitations and abilities, or "specs", of Geass are listed here.
All that is known of the background of Geass is that the form which we see it in currently was developed or discovered by army researchers under commands of Prince Clovis through Bartley Asprius. The project seems to have been named "Code R" and was valuable enough to Clovis to use his Royal Guard to protect and important enough to warrant the utter destruction of Shingiku. The Geass power is clearly connected or controlled in some way by C.C., but who she is is unknown.
Outside of the above knowledge, there have been hints about the origin and history of Geass. When C.C. explains her contract to Lelouch, he sees a vision of many people, seemingly children, standing in formation all bearing on their foreheads the same mark as C.C. Then, the Britannian Emperor is shown angrily saying "..a convergence with the Ragnarok connection? So the myth is beginning once again?!" It is difficult to say what these images might mean, but they open up a number of possibilities for the origin and history of Geass.
The only user of Geass is Lelouch. Even C.C. cannot use Geass.