Originally Posted by
Vacant
I believe it is defined to denote possession or association, the difference being that possession either denotes something one owns or something which belongs to one, while relation merely notes something that is related to one. In this sense, it's more related to the example of a "children's department" in a store; the children certainly do not own the department, nor is it exactly correct to say it belongs to them. It is, however, the "children's department" all the same, since the goods sold in that department are associated with children. Not that it really goes against the overall point, but just sayin'.
In other words, "my girlfriend" is not the girlfriend I possess, but a person who is a girlfriend and is associated with me. Or at least that's how I'd rather think of it, anyhow, hence my problem with using "mine," since that carries a an exclusively possessive valence insofar as I'm aware.