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.