Galileo contributed to the Renaissance by helping to create a new way of thinking. In this new way of thinking, people did not simply trust in what they had been told by religious authorities or by ancient thinkers like Aristotle. Instead, they required scientific proof of things if they were to believe them.
Galileo helped bring this sort of idea about by doing many experiments and observations to determine how things really worked. For example, he did his famous experiment to prove that objects of different weights fell at the same rate. Galileo also created the first telescope that could be used for astronomy. Using the telescope, he took observations that he could use, for example, to prove that the planets were moving around the Sun and not around the Earth.
The Renaissance was a cultural movement that initially began in Florence, Italy, but later spread throughout Europe. It started around 1350 and ended around 1600. During the Renaissance Era (a word that means "rebirth"), people experienced changes in art, science, learning, and many other things.
Galileo Galilei (1564-1642), was considered the father of modern science as he made important contributions to physics, astronomy, mathematics and many other scientific areas during the Renaissance Era. Notably, he improved the telescope and discovered parts of the universe not yet seen before, like Jupiter's moons and many new stars.
Although Galileo was largely disliked by the Catholic Church during this time, he continued his pursuit for correct knowledge about the universe. He agreed with the heliocentric model of the universe, first proposed by Nicholas Copernicus, and in doing so was placed in jail for the last years of his life.
Galileo set the stage for Issac Newton to create further advancements in science and mathematics.
Galileo Galilei (1564-1642) was an important figure in Renaissance-era Italy, a mathematician and scientist who's contributions to astronomy and physics were outweighed only by his role in advancing the concept of scientific fact as more determinative of reality than dictates handed down by the Church. His observations of the night sky and contributions to the development of the telescope helped immeasurably in proving that, in contrast to the ancient theories of Aristotle, which were supported by the eminent astronomer Claudius Ptolemy, that the Earth was the center of the universe, that the Earth, as with the other identified planets, orbited the Sun. The heliocentric theory of the solar system had been most prominently advanced by Nicolas Copernicus, but Galileo's efforts were important in reaffirming his predecessor's theories.
Galileo conducted numerous experiments and made a number of inventions that further contributed to the advancement of the sciences. His struggles, as a devout Catholic, to reconcile Church Doctrine with respect to the structure of the universe with his principles as a scientist caused him to repeatedly run afoul of Church authorities. While he was not subjected to the extreme and extremely painful measures defiance of Church orthodoxy often entailed, he was kept under a great deal of scrutiny for his belief in science-obtained knowledge, but was ultimately confined to house arrest for the final years of his life.
To the extent the Renaissance era was characterized by major advancements in science, as well as the arts, Galileo was an important figure in facilitating those advancements.