I think that probably Galileo's most important contribution to the Western world was to help undermine the idea that religious belief should determine scientific facts. By sticking to his guns when the Church opposed him, he helped us towards the important idea that religion and science should be separate. (This is being eroded some in the US right now...)
Galileo is also important because of his invention of a telescope that could be used for astronomy and for his proof that objects of different weights fall at the same rate. Both of these were important scientific discoveries.
Galileo (1564-1642), was astronomer and physicist, who is considered to be the founder of modern experimental science. Also he discovered and popularised many scientific facts that challenged many beliefs false beliefs common among people of his time.
Galileo built in 1609 the first telescope to discover important new facts about astronomy. He used this to collect evidence that many of Aristotle's and Ptolemy's claims about the heavens were false. His first discovery was that, far from being perfectly smooth as believed earlier, the moon was mountainous and pitted, much like the earth. His most sensational discovery was in 1610, when he discovered four moons circling Jupiter. His observations of heavenly object confirmed his belief in the truth of Copernicus's theory that the earth and planets revolve around the sun. Publication of these findings by him, starting in 1610, brought him wide renown and also brought him in direct confrontation with the Roman Catholic Church.
He also discovered the law of falling bodies as well as the law of the pendulum. He demonstrated that all objects fall at the same speed, regardless of their mass, and that pendulums of equal length swing at the same rate whether their arcs are large or small.
Galileo designed a variety of scientific instruments. His approach to scientific problems has also influenced substantially the method of scientific studies and opened the way for the development of modern mathematical physics. His method involved reducing scientific problems to simple terms on the basis of everyday experience and common-sense logic, and then analysing and resolving them according to simple mathematical descriptions.