Property is a type of possession. We usually think of property as "real property" (a house, building, land, etc.). Property can also be "personal property" (jewelry, a car, a computer, etc.). Example: I own beachfront property. Possession is a more broad term for something you own. A man may claim his wife as his possession (though this isn't considered political correct in most countries today). Example: My thoroughbred race horse is my most prized possession. Ownership is the state of owning something. Example: I have/took ownership of my father's house since he died.

Property is something you own, though it often refers to a house. You have possession of something if you possess, or have it. You have ownership if you own something. It is possible to possess something that you do not own, or own something that you do not possess.