I have read that our cells are constructed in a way that limits the number of times that they can divide. This isn't just a limitation on humans. All sexually reproducing creatures share this trait. The explanation for this, as I understand it, is that a body has a certain amount of energy to divide between continuing the self, creating the next generation, etc. Aging and death are an optimization that evolutionary processes have arrived at.
Otherwise, bodies are fragile, easily destroyed by accident, predators, or acts of willful destruction.