Answer:
'Tetrarch' originates from 'tetrarchy', which is a system of government where power is divided among four individuals. Tetrarchy most commonly refers to the government of the Roman Empire when it was reigned by Diocletian.
Then, the four Tetrarchs based themselves not at Rome but in other cities closer to the frontiers, mainly intended as headquarters for the defence of the empire against bordering rivals. It was an appropriate measure at that time because enemies on all sides was threatening the empire, but the king couldn't be at two or more wars at the same time. It was dangerous to delegate a subordinate general military power as well, since he might win a victory and then be proclaimed as a rival emperor himself by his troops (which often happened).