The way a tree dies is through not getting enough nutrients and water through it's roots.
The roots of a tree are like the blood vessels in our body and when the tree needs water they suck up water through the roots and sends it through the trees body.
Then also the tree gets nutrients through those roots as well.
Eventually those roots may get so old and bad that they cannot get the water and nutrients through the roots that they need.
So eventually the tree dies.
Most trees die of old age when they are 100 years old or more but sometimes trees can live as long as 1000 to 5000 years and longer.
But eventually all trees will die.
Also the only way a tree will die suddenly is through a weather event such as lightning, high winds, ice etc that topple a tree or rainfall that uproots a tree.
Another way that trees die is by girdling themselves because they get too big, or something unpleasant gets sucked up in their roots.