The geocentric theory was the paradigm that the Earth was in the center of the universe. Around Earth, which rests in the center, revolved the heavenly bodies, the planets and the stars.
The planets were first believed to revolve around the Earth in perfect circular orbits, with uniform speed. This belief was gradually backed down from as it was discovered that this could not explain the observations made. The epicyclic theory of Ptolemy tried to explain the planetary motions with circles on circles, then the centers of the circles were displaced slightly from the Earth, etc.
One can think of a number of observations, for example:
The varying speeds with which the planets move across the sky. An even more severe problem is:
The retrograde motion of the planets, where a planet makes a little ``loop'' on the sky during the course of a few months. This happens when Earth ``overtakes'' one of the outer planets on its way around the Sun.
The fact that Venus and Mercury are never found far away from the Sun indicates that they are orbiting the Sun, not the Earth.
The fact that Venus shows a full range of phases.