What does this mean?: “IF only she were mine”

No comments on relationship. Though I had the same confusion when I for the first time came across "If I were...". I couldn't understand why it was "were" where I would expect it should be "was".
Then I was told that it was an old fashion figure of speech that is still used in English today in the conditional sentences, followed by a subordinate clause: "If I were.... I would...".
However there are many native English speakers here who can explain it better than me.

Nope, goossun... you explained it better than most native English speakers ever understand it. We typically just memorize that old construction (I think it was called the subjunctive, don't quote me on that) in the rare cases where it is needed, mostly with "if," as in, "if I were you, I'd...." I'm a good example of the trend toward NOT using it anymore, so to a very conservative grammarian, I get it "wrong" all the time.

"If only" means "I wish it was true that." It's usually used when the wisher thinks that the thing he is wishing for is not really possible (although it would be nice).

So if your boyfriend leaves a testimonial on the web about another girl (you did not specify who it was about) that says "If only she were mine," then he is really doing nothing more than admiring her from a distance. If he says that about YOU, though, maybe he wishes you would pay more attention to him.

American Herutage says: "Subjunctive: Of, relating to, or being a mood of a verb used in some languages for contingent or hypothetical action, action viewed subjectively, or grammatically subordinate statements."
Was that what you meant?

I thought it's worth to add that this "Were" and its conjugation for the first and the third singular person in the old English has to do with the old Germanic roots. There were no distinguishes of the verb "to be" for different persons as it has still remained the same in Danish for instance.
Angles have taken lots of these stuff into English when they migrated to "England" in the 5th century A.D. They were originally from where today is the Germany-Denmark border and there are lots of hints of southern Danish dialect in English that is sometime amazing.
I'd go so far to say that even the word Anglo-Saxon is a Danish dialect. The equivalent of the word "and" is "og" in Danish which is pronounced "O". "Angle og Saxon" I do believe was the original form of Anglo-Saxon.