Well, until you’ve asked her to be your girlfriend and she’s agreed — she’s not your girlfriend. That being the case, it’s not your responsibility, nor is it appropriate, for you to be talking to anyone on her behalf.
That said, if you want her to be your girlfriend — tell her that.
To answer your, “What is meant by “girlfriend”?”, question directly: Generally speaking when someone refers to someone as their “girlfriend” or “boyfriend” the implication is there is an exclusive relationship (as opposed to just “dating someone”).