An ancestor is a parent or (recursively) the parent of an ancestor. So this includes a father or mother, as well as grandparents, great-grandparents, and so on.
Two individuals have a genetic relationship if one is the ancestor of the other or if they share a common ancestor; in a curious use of language in evolutionary theory, this is called common descent. (Strictly speaking this may not be true for some bacteria and similar organisms which are capable of direct horizontal gene transfer.)
Some societies have had a form of ancestor worship; most modern societies seem to have focused this into genealogy.
See also