Inappropriately tells you how someone did something: they did it in a way that was not suitable or not right for that situation. It is the adverb of inappropriate, so it usually sits on a verb — speak inappropriately, behave inappropriately, laugh inappropriately — or on an adjective: inappropriately casual, inappropriately dressed. Adults use it without thinking it is a fancy word. Workplaces and the news use it a lot for comments, jokes, or touching that cross a line. Though actually the word is broader than that: a heavy coat in July, or a joke at a funeral, can also be done inappropriately. It does not mean “badly” in the sense of “not skilfully.” A person can do a job well and still handle one moment inappropriately.