Here, the Earth, E, is displaced slightly from the center, C, of the path of the planet. Although this construction violated the rule that the Earth was the center of the cosmos and all planetary motions, the displacement was minimal and was considered a slight bending of the rule rather than a violation. The eccentric in the figure below is fixed; it could also be made movable. In this case the center of the large circle was a point that rotated around the Earth in a small circle centered on the Earth. In some constructions this little circle was not centered in the Earth.
The second construction, the epicycle, is geometrically equivalent to the simple movable eccentric. In this case, the planet moved on a little circle the center of which rotated on the circumference of the large circle centered on the on the Earth. When the directions and speeds of rotation of the epicycle and large circle were chosen appropriately, the planet, as seen from the Earth, would stop, reverse its course, and then move forward again. Thus the annual retrograde motion of the planets (caused, in heliocentric terms by the addition of the Earth's annual motion to the motion of the planet) could roughly be accounted for.

But these two constructions did not quite bring the resulting planetary motions within close agreement with the observed motions. Ptolemy therefore added yet a third construction, the equant. In this case, the center of construction of the large circle was separated from the center of motion of a point on its circumference, as shown below, where C is the geometrical center of the large circle (usually called in these constructions the excentric circle) but the motion of the center of the epicycle, O, is uniform about e, the equant point. Ptolemy combined all three constructions in the models of the planets, Sun, and Moon. A typical construction might thus be as in the picture below, where E is the Earth, C the geometric center of the eccentric circle, Q the equant point, F the center of the epicycle, and P the planet. As mentioned before, the eccentric was often not fixed but moved in a circle about the Earth or another point between the Earth and the equant point.

Info taken from http://es.rice.edu/ES/humsoc/Galileo/Things/ptolemaic_system.html