from which an organism has descended.

Note that it really doesn't matter how many generations or years that one has to go back, so long as an organism is on the same lineage as the organism we are focussing on, and existed prior to that organism in question, then that organism is an ancestor. See also the concept of ancestor species.

Ultimately, though, the concept of ancestor becomes one of descending from a population's or species' gene pool rather than necessary from particular individuals (though ultimately descending from particular individuals is true as well). Thus we can have ancestry in particular countries or regions of the world as well as among members of early genus Homo, or early members of family Hominidae, etc.

In addition, in sexually reproducing organisms it is possible to be descended from an individual and yet possess none of that individual's specific hereditary material, and this is due to a diluting of each ancestor's contribution to descendant organism genomes with each generation.

This is not to say that one does not share genes with ancestors, just not necessarily specific alleles that came directly from that individual. Yes, this means that it is quite possible to have children and for your children to have children, and so on, yet for your individual alleles to still not survive!