The ‘pink slip’ is one of the papers you need for the car. Pink slip is the coloquial name given to the Certificate of Title roughly in parts of US, Canada and Australia. In short, it is the car title, which says that the vehicle belongs to a certain person, so it states the owner of this vehicle.
I think the equivalent in Spain would be “el permiso de circulación”.
The name comes from the colour of the paper in the past, although now apparently it has changed, but the term is still common.