The stars appear to move in circles about a line through the poles of the earth. An ancient explanation of this (probably predating classical Greece) is that the stars are attached to a sphere which rotates about the earth. Aristarchus of Samos (third century BC) explained the apparent motion of the stars and planets by proposing that the earth turns on its own axis and also travels around the sun. Hipparchus (second century BC) and Ptolemy (second century AD) rejected this view for two reasons. First, one cannot feel the rotation of the earth. Second, one cannot (without powerful telescopes) see annual changes in the relative position of the stars. The earth-centred view dominated European science until the seventeenth century.
Whether or not the earth moves used to be an important question for Christians, as well as cosmologists. Giordano Bruno taught that the earth moved. He held a range of heretical views and was charged by the Holy Inquisition in Venice. He was sentenced by Pope Clement VIII and was burned alive, with his tongue gagged, in 1600. Galileo also taught that the Earth moved. He was charged with the same heresy in 1633 but he was spared on condition that he renounced his views. (The Vatican has since changed its position: in 1992 Pope John Paul II officially expressed regret at the church's treatment of Galileo.)
The observation of Hipparchus and Ptolemy that one cannot feel the rotation of the earth is correct. However, the rate of rotation required for the heliocentric picture (0.0007 revolutions per minute) is so slow that one would not expect to feel it. How can one measure such a slow rotation? In 1851, Jean-Bernard-Leon Foucault suspended a 67 metre, 28 kilogram pendulum from the dome of the Pantheon in Paris. The plane of its motion, with respect to the earth, rotated slowly clockwise. This motion is most easily explained if the earth turns.