| The person next in line to inherit something passed down by blood line, such as a lordship, and who cannot be overtaken by any subsequent birth, as opposed to an heir presumptive, who is next in line but might not be so in the future.
Note that the term heir strictly means one who has inherited something (by blood descent), not someone who is due to when in the future someone dies.
Normally a female cannot be an heir-apparent, because there is always the (at least theoretical) possibility that a son will be born to the present holder. But there is one way in which this can happen. Suppose a lord has an eldest son. That son has a daughter, but then dies before his father. He was formerly the heir-apparent; that position now passes to his daughter. Because her father is dead, he can never have a son who will subsequently dispossess her. So she is guaranteed to succeed (if she lives).
By 'normally' I mean that traditionally, in most European systems of inheritance, younger sons inherit before older daughters. It depends on the country. In France the Salic law prevented any female inheritance to the throne; in Denmark and Sweden in recent generations the law has been changed to allow succession to the throne in order of birth.
English peerages very seldom allow any female holders (the exact nature of who may inherit them is specified in the patent creating the peerage); in Scotland you often do get female peers in their own right, but sons still inherit before daughters. And (in England at any rate) there can only be one daughter as heir: if there are two or more, the peerage goes into abeyance between them until only one heir is left alive. But this is not true of the throne: Elizabeth II inherited solely, despite having a sister Princess Margaret. A recent proposal in the House of Lords to change the two British systems (English and Scottish) was defeated.
Thanks to gn0sis for suggesting clarification on Scandinavia, and to Rudra for pointing out the Salic law applies only to French royalty, not nobility. | 
