The issue of generations is twofold. First, the probability of contamination increases with each passage and, if it has occurred, it is going to become more prevalent with each passage (this is probably the most critical issue for home brewers). Second, the probability of genetic change from the starting population increases with each passage and if a change occurs that gives a growth advantage it will be amplified with each passage. Both issues have to do with maintaining the strain in a state that reflects that of the starting population which was probably genetically identical and pure.
Notice I say passage. That is probably a more correct way of saying it than generation. A generation implies one round of division and, as someone has already pointed out, that occurs many times per brewing. A passage is one round of growth to full density.