An absolute monarchy is a country that is ruled by a monarch, with little or no democratic or other forms of limitation to his powers. Quite rare in the modern world, examples include: Saudi Arabia and, until recently, Kuwait and Nepal.
Contrary to popular opinion, absolute monarchies were never the norm in Medieval Europe, where some form of representative bodies always tended to exist. 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. In Great Britain (from 1801 the United Kingdom), on the other hand, went in totally the opposite direction, and the monarchs were gradually stripped of their powers until very few remain today.
The Roman Empire, though it started out as a republic, 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.