To gyrate is to revolve around a point or axisor to oscillate with or as if with a circular or spiral motion.

Often used to refer to the process of orbiting one's hips around the center of one's mass along the z-axis (if one pictures the ground as a Cartesian coordinate plane).

One notorious source of gyrative imagery is the Squaresoft game |Xenogears|, in which giant robots suggestively, and constantly, sway their lubricated steel hips.