Possessiveness is often described as an undesirable trait and, in fact, the obsessive, controlling type of possessiveness is terrible. When you meet someone who wants to treat you like a possession, you should run (unless you want someone to command your every move but that is another blog entirely).
There is an upside to possessiveness-within-reason. It is a manifestation of your investment in someone’s life. Being possessive benefits the relationship when you want what is best for the other person (hint: they have to want it, too). It can keep you present in the relationship and interested in the life of your partner. It can increase the intimacy and the commitment within the relationship.
However it is a thin line between possessive and possession. Be on your guard to ensure that neither of you is attempting to control, manipulate, or guilt the other person into doing something. Use possessiveness as an asset, rather than a liability.