Are you on your own means different things in different situations, but it always means 'alone / by yourself / not accompanied by anyone'. Do you live on your own? (alone) Are you here at my party on your own? (by yourself) Have you travelled all this way on your own? (by yourself without anyone accompanying you) Did you compose this question on your own (i.e., without anyone's help) :)

Yes, exactly.

You are not living with your parents, family, or a partner.