Literally, a circle on a circle . See figure 1.25 on page 41 . Think of it as a long arm moving around with a smaller hand swinging around at the end of the long arm. That is, this determines the rate at which the planet crawls over the sphere of stars, that sphere of stars causes the planet to rotate about the Earth daily. The planets always move east to west across our sky relative to the horizon.
Different planets require epicycles of different sizes.
In the geocentric model, when planets have their epicycles must be correlated to the sun. Hence in the geocentric model, the centers of the epicycles of Mercury and Venus are assumed to stay aligned with the sun. Note that this model is starting to become more cumbersome, we keep having to add additional rules. Ptolemy's model predicted planetary motions pretty well for the next 1400 years. Pretty well, but never perfectly.