The term means the father and ruler of a family or tribe--literally, "rule of the father." It's used in two senses.
When we're speaking about the Old Testament, it refers to Abraham, Isaac, and Jacob, since they were the fathers of the Jewish people.
When we're speaking about Christian times, patriarch refers to a prelate who holds precedence over primates, metropolitans, and bishops. In order of dignity there are the patriarchs of Rome, Constantinople (modern-day Istanbul), Alexandria, Antioch, and Jerusalem.
There are also patriarchs of the Armenian, Maronite, Melkite, and Chaldean rites (all Catholics), and there are "minor" patriarchs in Venice, Lisbon, and in the West and East Indies.
Aside from the patriarch of Rome, who is the pope, the patriarchs have no power greater than that held by other bishops, but they have greater honor because of the history of their sees.