On a pope's reignA user known as Gaucho writes:
Why do Catholics speak of a pope's tenure as a reign? It does sound tacky.
A Pope's tenure of referred to as a reign for three reasons:
1. A Pope is, in fact, a temporal monarch. He is the Supreme Authority within the Vatican State. If that tiny realm doesn't seem like enough to reign over, it is important to remember that it is actually a tiny remnant of a much larger state which included all of central Italy, which the Holy See had authority over until Italian unification, and which the popes claimed as their legitimate sovereign territory until the signing of the Lateran Treaty in 1929.
2. The Pope serves as the Supreme Head of the Church on Earth, more commonly called the Supreme Pastor. Catholics believe that Christ is the head of the Church, of course. Since Christ obviously hasn't returned yet, the Successor to Peter takes care of the Church's earthly affairs, such as seeing to the financial and social stability of Catholic Christian communities around the world. The Pope also is at the head of the Church's worldwide missionary work, funded by an annual collection called Peter's Pence.
3. The Pope is the leader of the College of Bishops throughout the world. A bishop's religious authority is supreme within his diocese. The only authority higher than a local bishop is that of the Holy See.
Hope this explanation is a help.