I think they learn it from us, I know that I say "that's my coffee, you can't have my coffee, it could burn you blah blah blah" "That's my/mama's computer, you can't play with my computer it could break blah blah blah" so they pick it up pretty quickly that "ownership" is a powerful tool.
Ds is 29 months old and is really focused on the ownership of items, whose shoes are whose, whose hat etc (we live in a house of 8 people, 7 adults and ds, so there are a lot of "things" and I think ds' knows "whose" almost everything is)
When he says things are "mine" or even "yours" or "so and so's" but they are in fact things everyone can use, a chair, a glass, a book etc. We usually say, "actually that belongs to everyone, or it belongs to the house (or at school, it belongs to the school) but you are currently using it" or something like "that cup is for everyone, but right now, yes mama is using it" or he says "my ball" and I say "that is the ball you are using"
pretty much though if it is *hers* I would acknowledge it, as she is trying to order the world, also if its the yell of "mine" complete with snatching (oh how I love that!) then I would address the "snatching" more than the word usuage.