Living Tree

Giant Trees (aka Living Trees) are huge trees that can be found on the surface of a world and are created during world creation. Unlike regular Trees that can be found growing across the Forests, these Giant Trees cannot be passed by the player, have trunks several blocks thick, and reach staggering heights into the air. (On Small worlds, they can even reach Space, where Harpies begin to spawn.) Underneath, you will either find large roots blending with the dirt or a long vertical tunnel which reaches a house-like area which contains Living Wood furniture and a Living Wood Chest which can contain either a Living Wood Wand (for placing Living Wood) or a Leaf Wand (for placing the leaf blocks.) This tunnel will often continue a distance further down, only stopping when it hits an opening in the earth, similarly to Pyramids in the Desert.

Building Giant Trees
Players can create Giant Trees after world creation by using the Living Wood Wand, Leaf Wand, and copious amounts of Wood. The player can craft Living Wood Wall by standing near existing Living Wood. (Some form of Grappling Hook or an accessory which allows flight is recommended for building trees of considerable height.)

As of 1.2.3, Living Wood Wall is crafted at a Living Loom.

Trivia

 * These Giant Trees seem to be based off of the tree built by developers in the first Terraria trailer.