The Acorn is an item that is dropped when cutting down Trees. For every leaf bush on a Tree, there is a chance to get one Acorn, and the chance is highest with the leaf bush at the top. However, cutting off a branch with a leaf bush on it will always give you one Acorn. Acorns can be planted and will eventually grow into Trees. If you have played on a single world for a long time and have cut down all the trees, it is advised to stockpile these.
When planting Acorns, remember to leave them enough space for them to grow, 3 blocks each is enough.