Malicious compliance is the art of being completely compliant with another person's wishes - to the point of being malicious about it. This is one of those wonderful little things I learned from the Navy. I think it's one of those things that comes about as part of a social system where you're expected to do what you're told. Even when it's something dumb, or you don't like the person giving you the order. I've used it as a disciplinary tool against superiors who don't know my job as well as I do.
The whole concept is best characterized by following the very letter of the law, if not its spirit. And not deviating even a single iota from whatever it is you've been told to do. The classic example I like to give involves monitoring some important panel, and doing some important work. The person actually operating the panel or station does something without informing his immediate supervisor. The supervisor gets annoyed, and like a good little officer, issues an order. This will typically be along the lines of 'don't touch anything without telling me first'!
Any experienced officer probably realizes that saying this is probably a bad idea without some kind of qualifier. However, now you've annoyed the technician who is actually operating the equipment and probably knows better. Ideally, he should only report when he's operating something critical. Instead, in the true spirit of malicious compliance, he's going to tell the officer when he touches -anything-. Even if it's changing where he's resting his hands.
This can be funny to see in practice, and frustrating to the guy who was just trying to look after his own ass.