Why do cells have an average 'life span'
We refer to the number of times the cells of an organism can possibly divide as the Hayflick limit for that organism. The Hayflick limit serves as a theoretical life span, because telomeres (on the ends of chromosomes) get slightly shorter with each round of division, until they are gone completely. Telomeres are put on the ends of chromosomes by the enzyme telomerase, which is abundant in infants (who are growing and undergoing rapid mitotic divisions) but bodily abundance of the enzyme quickly diminishes with age. Without telomeres, our actual chromosomes would shorten in length during each round of division -- essentially, this is what happens after the telomeres are eroded away at in the later years of life. The Hayflick limit for humans is given to be 120 years -- with perfect self-care, 120 years of life is possible.