Civility is the act of showing regard for others by being polite, like the civility you showed in speaking kindly to someone who has hurt your feelings.
Civility comes from the Latin word civilis, meaning "relating to public life, befitting a citizen," in other words, being friendly and nice to everyone. When you show civility, you use kindness and good manners. You are respectful, even if you do not like that person very much. Civility can also mean formal politeness, like your behavior at a fancy dinner.