Tycho believed that the earth was fixed in the center of the world.
Around the earth circulated the moon and the sun.
Around the sun orbited the rest of the planets.
He based this view mostly on measurements of the apparent movement of Mars,
and he did not think it was explained by the traditional ptolemaic geocentric
world system, where the earth was in the center and everything orbited
around the earth.
Tycho Brahe was born three years after Copernicus had publishes his revolutionary work, "De Revolutionibus Orbium Coelestium", which put the sun in the center of the world, and all planets including the earth orbit around it. This is called a heliocentric world system. Tycho Brahe thought Copernicus was a brilliant astronomer, but he did not accept his world system, primarily for religious reasons. The church stipulated that the earth was the center of the universe.
Even if Tycho's world system was not widely accepted, it can be said to be important in such a way, that when Tycho Brahe tried to prove his world system by observations, he made a table of planetary movements. These tables were later completed and used by his assistant Kepler to make his famous planetary laws, which showed that Copernicus was right, the sun was the center and the planets moved around the sun. But the planetary movements were elliptical not circular, something which Kepler first thought was absurd, but he to had to accept it, since Tycho's accurate measurements confirmed this theory.
Picture of the Tychonic World System, including the known planets of the time, with Saturnus being the furthest from the Sun. Inside the stars are the twelve signs of the zodiac.