Being civil is the recognition that those you interact with are also human beings and deserve to be treated as such. It means striving to not demean or attack, to remain polite (yes, politeness is superficial, but it's also important), to listen, and to accept. It means being able to agree to disagree, and that the "other" isn't a moron because they disagree with you. Maybe they're wrong. Maybe you are. Are you a moron because you were wrong?
It doesn't mean never losing your temper; it means not treating people you're angry with like crap. You don't have to call someone an "idiot" to treat them like idiots. Being rough around the edges or using strong language isn't a problem, routinely telling people you disagree with to "fuck off" is – not because you used the word "fuck", but because it shows lack of respect.
In the end, it's all about treating other editors as peers, not as plebs that can't possibly understand your genius, or as adversaries. That is what the civility pillar is about: work with each other.
Although I work for the Wikimedia Foundation, contributions under this account are exclusively in my individual, personal capacity.