This is the kind of kiss you give your girlfriend or wife if she's spent too much time casually flirting with that tall, dark stranger (who might or might not be handsome, you really couldn't say.) The possessive kiss can be anything from a passionate kiss to a little peck on the cheek. Often a possessive kiss is accompanied by a throwaway term of endearment like "honey" or "baby" or "lover".
The purpose of this sort of alpha male behavior is to essentially tell the other guy, "Back off. This is my woman." Not suprisingly, this usually isn't particularly well received by the woman. (Then again, two weeks later you'll be nailed to the wall for your inability to engage in public displays of affection, so who knows? :)
Of course women also are equally guilty of dispensing possessive kisses.
Back to the Kissing Metanode.