A society that's monarchical is ruled by a king or queen. In a monarchical state, rulers inherit their power from their parents or other relatives.
Some monarchical states are known as "elected monarchies," in which citizens elect a monarch, but most have been hereditary, with monarchical rule passing from parent to child, and lasting for the ruler's lifetime. This style of government is unusual today, though it was common before the nineteenth century. Most remaining monarchical countries, like Great Britain, are constitutional monarchies, in which the king or queen has a ceremonial role. The Greek root word is monarkhia, "ruling of one."