The Great Deku Tree is the guardian spirit of the forest. When Link defeats the evil Queen Gohma lurking inside him, Deku Tree knows that Link is the boy who will save the Hyrule from Evil, and gives him the Kokiri's Emerald.
The Great Deku Tree was cursed by Ganondorf and Deku Tree died in that. After seven years passed and Link broke the curse in Forest Temple, the Deku Tree Sprout grew to the forest, and he might be the Deku Tree from The Legend of Zelda: The Wind Waker, though that is no sure information.