उसका / उसकी means "that one's own", in other words, "his/her/its". अपना / अपनी is often translated as "one's own" - that's not quite what it means, but it is an easy way to remember it. I believe it really means "my/your/his/her/its own", and is used to indicate when something belongs to a person just referred to, like when we say "my OWN room", मेरा अपना कमरा. The endings in the simple singular case are typically आ for masculine (or ए in certain other cases) and ई for feminine. When no gender is specified, masculine is default.
Hopefully if this isn't right, it will be corrected, or maybe someone will give better examples.