Short answers, pulled from the story.
Galileo Galilei was an Italian astronomer, physicist, and engineer, born in Pisa on the 15th of February 1564 and died on the 8th of January 1642. Albert Einstein called him the father of modern physics, and Stephen Hawking judged that he bears more responsibility for the birth of modern science than anybody else. He has been called the father of observational astronomy, modern-era classical physics, the scientific method, and modern science.
With an improved telescope he built, Galileo observed the four largest moons of Jupiter, the full set of phases of Venus, sunspots, lunar craters, and the stars of the Milky Way. On the 7th of January 1610 he first saw Jupiter's moons, and from September 1610 he observed the phases of Venus, which made the Ptolemaic model untenable.
Galileo was tried by the Roman Inquisition because he championed Copernican heliocentrism, the view that the Earth moves around a motionless Sun, which the Church declared formally heretical in February 1616. His 1632 book Dialogue Concerning the Two Chief World Systems appeared to advocate heliocentrism and to mock Pope Urban VIII, leading to his trial in 1633.
On the 22nd of June 1633 Galileo was found vehemently suspect of heresy, forced to abjure his opinions, and sentenced to imprisonment that was commuted to house arrest for the rest of his life. He returned to his villa at Arcetri near Florence in 1634 and went completely blind in 1638.
Galileo published Sidereus Nuncius, the Starry Messenger, in March 1610, The Assayer in 1623, the Dialogue Concerning the Two Chief World Systems in 1632, and Two New Sciences in 1638. Two New Sciences, concerning kinematics and the strength of materials, was published in Holland to avoid Catholic censorship.
The story that Galileo dropped balls of different masses from the Leaning Tower of Pisa comes from a biography by his pupil Vincenzo Viviani. There is no account by Galileo himself, and historians generally accept it was at most a thought experiment of 1589 that did not actually take place; most of his experiments with falling bodies used inclined planes.
Official Church opposition to heliocentrism faded over centuries, with all such works dropped from the Index of prohibited books in 1835. On the 31st of October 1992, Pope John Paul II acknowledged that the Inquisition had erred in condemning Galileo for asserting that the Earth revolves around the Sun.