The Pope is the Bishop of Rome, a position that makes him the leader of the worldwide Catholic Church which is composed of the Latin Rite and the Eastern Catholic Churches in full communion with the see of Rome.
The Pope is one of the church leaders around the world that agree to disbar Stan Smith from all religion after he beats up Roger in "Season's Beatings" when he discovers Roger got the role of Jesus Christ in the church play at the Langley Falls Shopping Mall that Stan wanted. When footage of the beating makes the news, church leaders around the world are stunned.
Unlike his Family Guy Italian counterpart, American Dad's Pope is a fairly faithful likeness to then-current Pope Benedict XVI.
A more generic image of a Pope appears in "Shell Game" when the Smiths adopt Italian mannerisms after trying a new kind of spaghetti sauce.