In ice dance (or more generally, figure skating, but dancers are usually the only ones who do them) a way of changing direction and feet at the same time. It consists of two steps, and the change of direction (forward to backward or vice-versa) occurs at the same time as the change of feet. It is contrasted to a mohawk in that the skater changes edges at the same time as he changes feet.
The first choctaw a dancer learns is in the Blues. Here the first step is a left forward inside edge and the second is a right back outside edge. The first edge is held for two beats, then the skater brings the right foot in to the heel of the left foot and brings the lean to nuetral. The skater then steps onto the right foot on a back outside edge. Good dancers will have extremely deep edges going into and coming out of the choctaw.
The choctaw is considerably less intuitive than a mohawk. A skater probably won't start working on it until they've been skating for at least a couple of years. However, it looks really cool when done well.
I don't know the derivation of the word in this context. In fact, it seems pretty absurd, but then, much of skating seems that way. Any ideas?