An heiress is a female who inherits wealth following the death of a relative. Often, the amount of wealth that an heiress inherits is of substantial or great value. This is why the term heiress is often used in reference to the inheriting of a fortune.
Heiresses usually have relatives, primarily parents, who have accumulated a large amount of wealth. For example, consider Paris Hilton. When her parents pass, she will be an heiress. Heiresses are the female equivalent of heirs. Heirs are simply males who inherit wealth in the same way that heiresses inherit it.