Hereditary Rule is a form of government wherein the rulership is passed down from one member of the family to the next. This kind of succession is most often associated with monarchical rulers, but it occasionally appears in despotisms or even purportedly communist regimes - North Korea, for example. There is often a religious justification for hereditary rule; kings are said to rule by "divine right" or "the mandate of Heaven."
The strength of hereditary rule is that there is usually a clear line of succession, and thus perhaps less squabbling for power when the current monarch dies. (There are plenty of exceptions to this rule throughout history, of course.) Further, there may be a certain amount of familial pressure on the ruler to not mess things up too badly for the next generation. However, hereditary rule suffers the same kind of weaknesses as do all unelected rulers: the leader is not answerable to the people, and it can be extremely difficult to get rid of a bad one.