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.