The key assumption of the Geocentric Model was that the Earth was at rest in the center of the Universe and that all other celestial bodies revolved around the Earth. This model or theory was written down by the famous Greek philosopher Aristotle before the beginning of our era. It was used by the astronomer Ptolemy in his book the Almagest, which was the standard book of astronomy for about 1500 years. The Geocentric Model was adopted by the Catholic Church.
To be able to get reasonable predictions for the motion of the planets, the Geocentric Model requires the specification of the size and rotation rate of many circles, of which it was not clear why the sizes and rotation rates should be just those values.
As the science of astronomy progressed, it became clear that the Earth is in fact not the center of the Universe. The first blow to the Geocentric Model came when Nicholas Copernicus (1473 - 1543) showed that puzzling aspects of the motion of the planets followed naturally if you assumed that the planets and the Earth revolved around the Sun and that the Earth rotated around its own axis. That model, with the Sun rather than the Earth in the center of the Solar System, is called the Heliocentric Model.
Johan Kepler (1571 - 1630) deduced from accurate observations that the orbits of the planets are ellipses around the Sun rather than combinations of circles, and managed to link the period ("year") of each planet to its distance from the Sun in a simple formula.
Galileo Galilei (1564 - 1642) discovered the four great moons of Jupiter, using a telescope that he built himself. These moons proved that the Earth is not the center of all motion in the Universe. Galileo's support of the Heliocentric Model of Copernicus got him into trouble with the Catholic Church which had much power in Italy at the time and which held that the Bible supported the Geocentric Model. Galilei was put under house arrest for the rest of his life.
Isaac Newton (1642 - 1727) showed that the orbits of the planets could be understood as a result of gravity between the planets and the Sun. The Sun turned out to be many times more massive than all other things in the Solar System combined. His theories also successfully explained the motion of comets. Still, it was generally assumed that the Sun was in the center of the Universe.
Just before 1840, several astronomers first measured the distances to some nearby stars and found them to be very, very large. If you know the distance of a star and its brightness in our sky then you can calculate its intrinsic ("real") brightness corrected for its distance. Measurements and calculations such as these showed that the Sun is but an ordinary star, and that there are many much larger, brighter, and more massive stars. Around 1930, it became clear that the Sun is not in the center of the Milky Way but in the outskirts, and that the Milky Way does not fill the Universe but is just one of a very large number of galaxies.
Today we know that the Earth is a planet of modest size, orbiting an ordinary star in the outskirts of an unremarkable galaxy near the edge of a common supercluster of galaxies of which there are very many more throughout the Universe.
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