This isn't something I hear. But I know what it means. An acquaintance is not quite a friend, but someone you just casually know, or someone you just met. Telling someone that they are a 'treasured acquaintance' is a bit silly, since I think it just means they are a friend, without the person admitting to it. Anyway, it means they are one of the better people they almost-know only on casual terms, more so than anyone else they just casually know.

To treasure someone or something is to value them/it highly. Acquaintance is a weak form of "friend"; someone that you know, but may not be a close friend.