The tree in Nebuchadnezzar's dream is a symbol for his own self. He will go from being a great provider, someone showering prosperity on his people and providing over a massive Empire, to some deluded weirdo, running around on all fours in the woods and fields and eating grass. He goes from being a symbol of abundance and health to being a symbol of madness, waste, and ruination. That's tough, Nebs.
You can read the dream as a parable of the Fall of Humanity, applied to one specific Babylonian king. It's much the same way that Adam and Eve eat from an evil tree (The Tree of the Knowledge of Good and Evil) and are unable to eat from the Tree of Life (which actually does appear in the Book of Revelation at the end of time, when people are apparently allowed to eat from it). For his part, Nebuchadnezzar goes from actually being a good and healthy tree to becoming a destroyed and desiccated tree—a stump, really—and then to back to being a good tree, or a whole and healthy human being, once again. Except this time he has the knowledge of God's reality and presence.