The ancients looked at the sky and thought that they could see heavenly bodies rotating around the earth.  In the sixth century BC, Anaximander of Miletus theorized that the stars were mounted on the inside of a transparent spherical shell and that the earth was a solid sphere hanging in the center of this shell.  The Sun, Moon, and planets would have been mounted on other spherical shells.  Anaximander’s theories were often criticized in antiquity, but his idea of revolving concentric spheres would dominate the western cosmological imagination for millenia.   

Anaximander’s theory explained the apparent movements of the Sun and Moon tolerably well, but the orbits of the planets presented it with a challenge.  In particular, if we look at Mars and think of it as revolving around the earth, we will occasionally see it stop, back up, and make a loop in the sky.  The astronomer Hipparchus of Nicaea in the third century BC and the theorist Claudius Ptolemy in the second century AD were among those who developed a new theory, according to which the stars and other heavenly bodies moved as if they were mounted on transparent spheres, but spheres that were mounted on other spheres.  So the major sphere might make a cycle around the earth, but each heavenly body seemed to be mounted on a minor sphere that made a cycle (an “epicycle”) around a point on that major cycle.  A very clear animated illustration of Ptolemy’s epicyclic system can be found here.  Here are some more illustrations of this Ptolemaic system:

with descriptions: 

From an old edition of Ptolemy’s Almagest:

Below is a video showing how these systems of illustration might represent one hypothetically possible orbit.