An epicycle is a term from Ptolemaic astronomy. The epicycle was designed to explain retrogradation.
In the Ptolemaic system, the planets are assumed to move in a small circle, called an epicycle, which in turn moves within a larger circle called a deferent. Both circles rotate counterclockwise and are roughly parallel to the Earth's plane of orbit (ecliptic).
The deferent would be considered to be centered on the Earth (as the planet was believed to be in orbit around Earth... see: geocentric universe).
As viewed from Earth, the planets were visualized as moving eastward along the deferent. Most of the time, the eastward motion of the epicycle was in conjunction with the eastward movement of the deference. However, at times the planet would move along the epicycle in an opposite direction to the motion of the epicycle along the deferent. This would cause the planet to slow down and reverse course, ie. retrogradation.
