What is a republic, and when, how, and why did Rome turn into one?

A republic is a way of government, where the people get to decide who rules their country, or state or whatever. In about 509 BC, the Kings son, Sextus, raped a married woman. Soon after she commited suicide, and her husband, Collatinus, and his friends, Brutus and Valerius, were enraged. They sought out to avenge her death. The three men carried Lucretia's body down to the forum, the town hall type place, so the whole town could see what happened. The town was furious and the three men went after the King Superbus (the proud), and his son, Sextus. The men found the king and his son, and the king fled. The son, was killed by Collatinus and Brutus, and shortly after Collatinus and Brutus were elected, by the city, to become the "presidents".