Apoptosis occurs in a growing fetus. The fetus, when developing limbs, for example, has webbed fingers at first. If you look at your fingers now there are clearly spaces between them. This was not the case in the womb. Specific cells were signaled to undergo apoptosis to form the gaps between our fingers. Same with our toes and our tails in the womb. Do not confuse apoptosis with cytolysis. (apoptosis = cell "suicide", cytolysis = cell "exploding" due to excess of water, for example.)
p53 is a protein that, in humans, is encoded by the TP53 gene. The p53 protein is crucial in multicellular organisms, where it regulates the cell cycle and, thus, functions as a tumor suppressor, preventing cancer.
Apoptosis is the absolute end of a living cell's cycle and p53 is a protein regulating the cell cycle. (p53 activates apoptosis)