'Tu me manques' does mean 'I miss you'. It's one of those phrases that can't be translated word for word into English. In French, the concept of missing someone is expressed the opposite way round from the way we say this in English. The subject of the phrase - in this case 'tu' - is the person who is absent, and the object of the phrase - in this case 'me' - is the person who is feeling sad about it. The literal translation of 'Tu me manques' is something like 'You are missing to me', or less literally, 'Your absence is painful to me.' By the way, the majority of European language express the concept of missing somebody in the same way as in French, with the absent person being the subject of the phrase.

In French sentences work with what's call COD and COI soif you want you can understand the sentence like that : Who is missing me ? You Who is missing you ? I