The geocentric model of the cosmos is a paradigm which places the Earth at the center of the universe. Common in ancient Greece, it was believed by both Aristotle and Ptolemy. Most Greeks assumed that the Sun, Moon, stars, and planets orbit Earth. Similar ideas were held in ancient China.
In this model, a set of fifty-five concentric crystalline spheres were considered to hold the Sun, the planets, and the stars. These spheres (called deferents) revolved at varying velocities around the Earth to account for the rising and setting of celestial objects every day.
However, this simple model of the revolutions of spheres could not explain all astronomical phenomena. In particular, planets were observed to wander across the fixed fields of stars over time; mostly they wandered in one direction, but occasionally they seemed to reverse course. To explain this strange retrogradation, Aristotle claimed that planets were attached, not directly to deferents, but to smaller spheres called epicycles. The epicycles were themselves attached to the deferents; the simultaneous revolution of both sets of spheres created an occasional apparent reversal of the planets' motions across the skies of the Earth.
Ptolemy further modified this model to more accurately reflect observations by placing epicycles upon epicycles, creating an extraordinarily complicated--but fairly accurate--depiction of the cosmos. He also displaced the Earth from the center of the universe, claiming that, while Earth was enclosed by the celestial spheres, the spheres actually revolved around a point called an eccentric, which was near the Earth but not quite on it.
This elaborate theoretical system stemmed largely from one important observation. If the earth did move, then one ought to be able to observe the shifting of the fixed stars due to parallax. In reality, the stars are so far away that this motion is undetectable without careful telescopic observations, but the lack of parallax was considered the death of any non-geocentric theory for a thousand years.
The Ptolematic model is however incompatble with observations of a gibbous Venus. Observations such as this led to interest in the Coprenician system and the Tychonian system.