An absolute monarchy is a form of government where a country that is ruled by a monarch who has little or no democratic limitation to his powers. Quite rare in the modern world, examples include: Saudi Arabia, Brunei and, until recently, Kuwait and Nepal. There have been good absolute monarchs, for example, Israel's King David, and bad ones.
Contrary to popular opinion, absolute monarchies were never the norm in Medieval Europe, but feudal monarchies. What happened was that after the end of the medieval period, some monarchies sought to increase their power, the prime example being France, which had indeed become an absolute monarchy by the 17th century. Louis XIV of France epitomizes the rule of an absolute monarch with his declaration "L'etat c'est moi. ('I am the state')".
The Roman Empire evolved into an absolute military dictatorship. Whether it was ever a hereditary monarchy, however, is debatable at best. While certain families did manage to found dynasties that lasted for two or three generations, the vast majority of emperors either came to power by a military coup, or in a few cases were appointed on merit by their predecessor.