What does it mean when he calls me his girl?

Anonymous
Ok, so I met this guy and I really, really like him. I'm not sure if he feels the same, there are sometimes I think he might. But my main question, and he has done this several times. There is another guy who's always hitting on me and I don't have feelings for him, Now when the guy I like finds out he will say something like, stay away from my girl/woman, don't talk to her etc. What does this mean? Or am I thinking too much into this?
What does it mean when he calls me his girl?
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