To civilize is to make someone or something more tame or refined, and less wild. A new police chief might try to civilize a city by cracking down on small crimes.
You can attempt to civilize your crazy dog, so you can invite people over without having her jump on them and chew on their shoes. You can also civilize a person by teaching them to be more sophisticated or tasteful: "My aunt tried to civilize me by taking me to museums and ballets, but I preferred watching professional wrestling on TV." The Latin word civilis is at the root of civilized, meaning "befitting a citizen" or "courteous."