A pink slip is a certificate for official automobile registration that proves the ownership of a vehicle. It is called a pink slip because the official document that is used by many DMVs is pink.
In the context of the law, whoever is formally registered on the pink slip, as the owner of the car, possesses the property rights of that car.
Pink slips can be extremely important in situations where it is necessary for the ownership of a vehicle to be authenticated. For example, if law enforcement has reason to believe that a vehicle has been stolen, then it may ask the driver of the vehicle to produce the pink slip to prove that they are the actual owner.
Pink slips are also needed when a sale of the vehicle has been made and the title needs to be signed over and given to the new owner.