what is an adverse possession?

Adverse possession is a way of acquiring property, generally real estate, without a voluntary transfer.  Although the rules vary by jurisdiction, and there are a lot of nuances and technicalities, basically if someone openly occupies property for many years (how many varies by jurisdiction, but generally at least 10) without the true owner's permission, and the true owner takes no action to claim the property in all those years, it becomes the property of the person who has occupied it.  In some jurisdictions the occupier must have acted under claim of right, in other words they must have had a reason to believe that the property was theirs and they weren't just trespassing.