The crescent kick is a kick (or leg technique to be fancy) taught in almost every martial arts system. It is one of the few straight leg techniques taught in most schools, and the only one that I know.
The crescent kick is performed by moving a straight, extended leg in an oval shape, with the strike coming usually at the top of the arc. It can be performed both inward and outward, and also spinning, flying, and even a combination of the two.
The actual use of the crescent kick is problematic. Since it usually requires a lot of commitment, and for the leg to be lifted well above hip level, it makes a bad street technique. My main use for it is it makes me feel like I am beautiful and athletic, like Michelle Kwan, and not just a clumsy person who puts a lot of effort into learning to fight people.
I have read some martial arts books that suggest the crescent kick is a good way to disarm a knife. It seems that trying to do this would be a good way to get your femoral artery sliced open.
In general, using the crescent kick for self defense is like joy popping...sure, there are people who do it, and seem to get away with it, but the chances are that most people would get hurt or killed if they tried the same thing.