I like to describe possessiveness as a desire to completely own and control. And when it has to do with another human being, to own and control all or most aspects of that person's life.
A lot of people are guilty of this especially at the beginning of a relationship, mostly because they are still getting to know each other and don't yet completely trust each other. Even at this stage it is not an excuse to be possessive and does not in any way show love.
This feeling of possessiveness must never be confused for love or being protective, it is totally different from those two. If someone loves you they would let you make your own decisions, they would give you your space, they would not question your every move or go through your calls to know who you 'be been communicating with and so on. Infact true love is setting that person free believing and trusting that they would make the right decisions for themselves and being there to pick them up when they fail.
Possessiveness in a relationship is very unhealthy and if not addressed can have very terrible consequences. With possessiveness comes jealousy and often times violence follows. I saw a true life program on TV a few days ago in which a groom stabbed his bride to death a few hours after their wedding because he saw her chatting with his cousin and got jealous. This chat with his cousin was not even going on privately, it was in full view of everyone, the wedding guests were still around. She was actually trying to hook up her cousin who told her she liked him. Now what is wrong with that? We all do that all the time. Her husband saw them talking, got upset and stabbed her to death and she was still in her wedding dress with their few months old baby in a crib nearby.
Nobody wants to end up this way but it happens.
Before going into a marriage, any signs of possessiveness has to addressed because it usually gets worse. If you still don't feel comfortable it is best you end the relationship before it becomes abusive because it definitely will.