Anything papal has to do to with the Pope, such as papal orders or papal ceremonies.
The Catholic Church is led by the Pope. His office is the papacy, and anything that is ordered by the Pope or involving the Pope can be called papal. The papal robes are ornamental and beautiful. The power of the Pope can be called the papal authority. Someone who represents the Pope is a papal representative. Anything papal can also be referred to as pontifical or apostolic, since the Pope is considered the modern version of Jesus' apostles.