Civil has several meanings. The simplest is cultured and polite, as in someone who is civilized. Civil can also describe things related to a community of people and their government, or a civilization.
If you work for the post office, you're a civil servant. The Civil Rights movement focused on the notion that all American citizens were entitled to the same basic civil liberties. Rather than getting hysterical, someone getting divorced should follow their lawyer's advice and be civil toward their spouse when they face each other in civil court over the matter of who would get the banana plantation.