The Hayflick limit (or Hayflick Phenomenon) is the number of times a normal cell population will divide before it stops, presumably because the telomeres reach a critical length.
The Hayflick limit was discovered by Leonard Hayflick in 1961, at the Wistar Institute, Philadelphia, when Hayflick demonstrated that a population of normal human fetal cells in a cell culture divide between 40 and 60 times. It then enters a senescence phase (refuting the contention by Alexis Carrel that normal cells are immortal). Each mitosis shortens the telomeres on the DNA of the cell. Telomere shortening in humans eventually makes cell division impossible, and it correlates with aging. This mechanism appears to prevent genomic instability and the development of cancer.