At the beginning of Ocarina of Time, Young Link must venture inside (via the mouth...) of him to purge whatever is ailing him. As it turns out, a giant Ghoma is causing all the pain. The Ghoma was sent by Ganondorf, in an attempt to take the Spirit Stone from him.
This causes the Deku Tree to die. When a Deku Tree dies, a seedling is born to take it's place. It takes a long time for a seedling to reach the sheer size of a Great Deku Tree in its prime. A second deku tree, possibly a seedling that took the place of the original in Ocarina of Time, is seen taking care of the Koroks in The Legend of Zelda: The Wind Waker. The mission of this Deku Tree is to spread the forest and greenlands to the remaining island to expand them and eventually revive the sunken land of Hyrule. This is only sort of possible.
The Deku Tree also shares a name with Deku Scrubs for some reason.