Diversity implies difference.
A diverse forest has many different species, both plant and animal. Often the more diverse a forest, the less chance there is that losing a single species will result in the loss of an entire forest. Many other species still survive and life goes on. Forest monocultures, or those with a single species, are more at risk from a new disease or insect destroying the entire forest. If there is only one species and it becomes extinct, you are left with nothing.