It doesn't orbit the Earth but rather one of the Earth/Sun's Lagrange points L4.
So it is a moon in the very loose sense that it orbits a point determined by the gravity of another body.
Consider Pluto/Charon. These two orbit around a point which is between them so they are really twin planets or asteroids (depending on your definition)
The orbit of Cruithne is not independant of Earth but it's not a true Satelite either.
There's a good page on it here - It's in French so this link is via bablefish
http://babelfish.altavista.com/babelfish/trurl _pagecontent?lp=fr_en&url=http%3A%2F%2Fmembres .lycos.fr%2Ffransyl%2Flagrange%2Fcruithne.htm
We keep finding objects in the solar system that don't quite fit into our old notional system of Star/Planet/moon/asteroid/comet and we don't have proper words for them so we end up banging them into a the nearest term that fits.
For what it's worth I'd not call it a moon but probably a Trojan-type object. after the similar asteroids called Trojans that orbit points about Jupiter