What is Pope?

Legal Definition
The pope (Latin: papa from Greek: πάππας pappas, a child's word for "father") is the Bishop of Rome and, therefore, the leader of the worldwide Catholic Church. The primacy of the Roman bishop is largely derived from his role as the traditional successor to Saint Peter, to whom Jesus is supposed to have given the keys of Heaven and the powers of "binding and loosing", naming him as the "rock" upon which the church would be built. The current pope is Francis, who was elected on 13 March 2013, succeeding Benedict XVI.

The office of the pope is the papacy. His ecclesiastical jurisdiction, the Diocese of Rome, is often called "the Holy See" or "the Apostolic See", the latter name being based upon the belief that the Bishop of Rome is the successor of Peter the Apostle. The pope is considered one of the world's most powerful people because of his diplomatic and cultural influence. He is also head of state of Vatican City, a sovereign city-state entirely enclaved within the Italian capital city of Rome.

The papacy is one of the most enduring institutions in the world and has had a prominent part in world history. The popes in ancient times helped in the spread of Christianity and the resolution of various doctrinal disputes. In the Middle Ages, they played a role of secular importance in Western Europe, often acting as arbitrators between Christian monarchs. Currently, in addition to the expansion of the Christian faith and doctrine, the popes are involved in ecumenism and interfaith dialogue, charitable work, and the defense of human rights.

Popes, who originally had no temporal powers, in some periods of history accrued wide powers similar to those of temporal rulers. In recent centuries, popes were gradually forced to give up temporal power, and papal authority is now once again almost exclusively restricted to matters of religion. Over the centuries, papal claims of spiritual authority have been ever more firmly expressed, culminating in 1870 with the proclamation of the dogma of papal infallibility for rare occasions when the pope speaks ex cathedra—literally "from the chair (of Saint Peter)"—to issue a formal definition of faith or morals.
-- Wikipedia
Legal Definition
The chief of the catholic religion is so called. He is a temporal prince. He is elected by certain officers called cardinals, and remains in power during life. In the 9th Collation of the Authentics it is declared the bishop of Rome hath the first place of sitting in all assemblies, and the bishop of Constantinople the second. Ridley's View, part 1, chap. 3, sect. 10.

2. The pope has no political authority in the United States.
-- Bouviers Law Dictionary
Legal Definition
The bishop of Rome, and supreme head of the Roman Catholic Church. 4 Steph. Comm. (7th Ed.) 168-185.
-- Black's Law Dictionary
Legal Definition
The head of the Roman Catholic church.
-- Ballentine's Law Dictionary