I am guessing you are asking why living things die from natural death at old age? and not e.g. via road accidents, being eaten by a predator, etc.?
Think about it this way, when you are young, you are very active, you dance, play football, run around, when you get injured you heal very fast…..but as you get older you feel more tired, become less active, sick often, etc. This is a reflection of what is happening within our bodies.
While we are young, our cells are active too. They divide very fast, make our wounds heals fast, just as jumpy as we are, clear infections fast. As we grow older, they slow down and because of this we become less active. The immune system in old age starts to fail and even simple infections like common cold becomes a big problem. At some point, our bodies either just shuts down because of disease or because the cells cannot further move on…and we die.
So, enjoy your youth now before your cells start slowing you down!
On a lighter note, and in addition to the answer by James, dying is also part of nature maintaining a balance in the ecosystem. Can you imagine of a world where all living organism never died, how can the ecosystem support such a population? There may not be adequate food, water, shelter for all living things to live on for long. Ever wondered how such a world would look like?
With technical advancement, better and healthy life styles, life expectancy in some regions of the world is increasing. Maybe there will be discoveries that can keep young for many years, and that can sustain other forms of life for long, ever wondered how long such a system can be sustained? Some food for thought.