"Civil twilight" means, "referring to the laws and regulations of ordinary life."
For example, let's suppose that the driving laws say that you must have your headlights on during twilight. What specific time period is meant by "twilight?" Very likely the law actually will use the words "civil twilight." If not, civil twilight is understood. Let's say you fail to turn your headlights on at sunset. A policeman tickets you and you try to appeal the ticket. You say to the judge "It wasn't really dark yet, I could see perfectly well, I didn't need my headlights." The judge says "According to this ticket, you were stopped at 6:11 p.m., and this online almanac says that on that day, 6:11 p.m. was during civil twilight. According to the law, your headlights needed to be on."
There is a very range of meanings for the word "civil." They all have something vaguely to do with "citizens." With regard to the law, there is civil law (e.g. suing somebody for not paying back a debt they owed you) and criminal law (e.g. murder). "Civil twilight" means "twilight, as used in the body of law called civil law." I can't explain why we say "civil twilight" instead of "legal twilight."
P.S. 1) In all my life, I can't think of any time when I ever needed to know the exact time period of "twilight." It's just the period when day is over but night hasn't begun. 2) With regard to "nautical twilight," in English, the world of seafarers, mariners, sailors, the Navy etc. is almost a separate subculture. There is a large specialized nautical vocabulary. On a ship, stairs become "ladders," floors become "decks," left and right become "port and starboard," and on and on and on. Distances are measured in "nautical miles" which are longer than "statute miles;" speeds in "knots" which are nautical miles per hour.