To pontificate is to talk in a dogmatic and pompous manner. To pontificate properly, you need to be a know-it-all with very strong opinions and the urge to share them.
Pontificate comes from the French word pontiff, another word for the Pope, the leader of the Roman Catholic Church. As a verb (pronounced pon-TIF-i-kate), it meant "to perform the functions of the Pope or other high official in the Church." The noun pontificate (pronounced pon-TIF-i-kit) refers to the government of the Roman Catholic Church. Another word for this is the papacy.