a governor: the official an empire appoints to run a province or region on the king's behalf
This is the Aramaic form of a borrowed administrative title, and it belongs to the world of imperial paperwork: royal letters, building permits, official summonses. Whoever holds the post holds it by appointment. Someone higher up hands him a territory and expects order, revenue, and loyalty back. He is never a king in his own right.
The word turns up in two settings, and they look quite different on the page. In Ezra it is a title fastened to a named man and a named place: Tattenai, the governor of the whole region west of the Euphrates, who rides down to Jerusalem to ask by whose authority the temple is being rebuilt, and the governor of the Jews, the local head of the small province of Judah. In Daniel it is one entry in a roll call, always plural, as a king summons or consults the ranks of his administration.
What holds the two together is that the word names a level of delegated authority rather than one fixed rung on the ladder. Tattenai and the governor of Judah both carry it, though one answers to the other. In Daniel's lists it stands third, after the satraps (אֲחַשְׁדַּרְפַּן) and the prefects (סְגַן), and below the three chief officers who report straight to the king (סָרֵךְ). The title tells you that a man governs a place for someone above him; the context tells you how large the place is.