In Greece and West Asia, mainly in what is now Turkey, there was a period of time around 650-400 BC when many city-states were ruled by tyrants. "Tyrant" is probably a Lydian word, from West Asia. Tyrannies usually grew out of oligarchies like this: in an oligarchy, each of the rich men is always trying to get more power than the others. But the other rich men keep them from doing it.
But if one of the rich men thinks of asking for help from the poor people, he can get ahead that way, and may make himself tyrant. So a tyrant is like a king, but a king who does not have the law or religion behind him, and only rules because the poor people support him. Tyrants are something like Mafia bosses like the Godfather.
Naturally the other rich men hated tyrants, and tried to stop them and go back to an oligarchy again. In order to stay in power, the tyrant has to promise the poor people that he will do good things for them, so they will support him. Usually the tyrant promises one or two of these things:
You can see that tyrants are usually really good for the poor people, and only bad for the other rich men. In English today, tyrant means a bad king, but that is because the rich men hated tyrants, and in ancient Greece only the rich men could write.