“Tetrarch” literally signifies one who is the governor (arch-on) of one-fourth (tetra) of a domain or kingdom. The Greeks first used the word when Philip of Macedon divided Thessaly into four "tetrarchies." Later on the Romans adopted the term and applied it to any ruler of a small principality that was permitted to retain some local control, while still being firmly under Roman rule.
The title was often conferred on Herodian princes by the Romans and was the legally accurate description of their office. While these Tetrarchs were subservient to Rome, they were permitted a great deal of liberty in how they ruled – frequently this was not in accord with the best practice of Roman law as we see in the beheading of John the Baptist by the drunken and lecherous Herod. For this reason, the Gospel accounts often calls them “kings” (Matthew 14:9 Mark 6:14); this is how the people – not the Romans—viewed them. In the same way a "tetrarchy" was sometimes called a “kingdom.”