Here are some examples of the word being used in a fairly everyday context. "It was police in Philadelphia though who started using the term 'Black Friday' in a more widespread sense in the 1960s, but for them it had a negative connotation." [Because it was associated with traffic problems]. "Yoga as a healthy activity free from religious connotation enjoys incredible popularity among people of all faiths." "[Disney] was quick to change its 'Moana' film title as soon as they learned its Italian connotation. Disney's Polynesian princess' 'Moana' shares her name with an Italian pornstar."

In my experience, "connotation" is used in spoken English when discussing the usage of words. It is formal. It's a good word to know when writing academic or high-level English. I'd expect a B2-level student to know or be willing to learn the meaning, and a C1-level speaker to use it reasonably well. One common expression is "negative connotation". Some words are not rude or obscene but they have a negative connotation in certain contexts or among certain groups. I remember a recent discussion on Italki about the use of the word "foreigner", which sometimes has a negative connotation.

A "connotation" is a halo of ideas and feelings that surround a word or phrase, even though they are not part of the actual definition. The definition of "apple pie" is a kind of dessert consisting of a hollow pastry crust filled with sweetened, cooked apples. In the United States, apple pie carries connotations of comfort, home, and (!) national identity (as in the phrase "as American as apple pie.") The definition of "lion" is a large, carnivorous feline with the scientific name _Panthera leo._ The word "lion" carries connotations of strength, masculinity, and nobility. The definition of "Wall Street" is "the street in New York that is the heart of the financial district." "Wall Street" carries connotations of power, money, and cutthroat, ruthless financial competition. It is not sarcasm or irony. It is also not a concealed meaning, as in "insinuation" or "subtext" or "reading between the lines." It's just an association that often goes along with a word or phrase. I'm a U.S. native speaker. I've used it in speaking and I've heard it used, both in the form "connotation" and "connotes."

Well, it's difficult to explain the exact meaning of "connotation", but at least in Spanish the term is quite often used, relatively speaking. I'd say everybody has heard about it at least once. What Steven said is correct, but let me explain it a little further. We use "connotation" when we want to add an additional meaning or nuance to another word (or a whole sentence), like a subtle sense that is not always explicit but somehow comes to your mind when you hear the word. For example, both "childish" and "youthful" refer to young people, but "childish" has a negative connotation as it could also mean "immature". Sarcasm is another example of connotation (maybe that's why you are confused, but it's not the only example), because you don't usually mean what you're actually saying, but the opposite. If I say: "please, tell me again how much your luxurious mansion cost, I didn't get it the last twenty times you told me" you could think I meant exactly what I said, but I said it in a sarcastic way, so the sentence has a connotation that implies that I don't want to hear anything about your mansion. I don't know if I helped, but in any case you can ask me again.

I not sure what your language goals are but the word "connotation" is a technical linguists term. In checking German translations (I speak German too) the same word appears to exist in German; but the German dictionaries also translate the words as meaning "associated with" or "meaning " in English. Having a pretty broad vocabulary in English, and being a 58-year old native speaker, I can assure you that the word is not used in the spoken language (in fact I've never even heard of the word in English -even used in writing) . If you're interested in the linguistic use of the word I'd simply check a exhaustive English language dictionary or one used in the study of linguistics. Sorry I couldn't be more help.