Possession usually means to have some sort of ownership over something else. A person may be in possession of some property, which is legal ownership, under property law.
There are some other related uses of the term. When English explorer, Captain James Cook, claimed the country of Australia as a British country, he took "possession" of the land. The spot where he made his claim on 22 August 1770, a small island in the Torres Strait, is now called Possession Island.