He predicts that the ring's power will consume them eventually, that it will change them into a slave of Sauron, and they will forever be under its power.  He uses the example of Gollum, and tells the story of how, before the ring, he was a normal being, and that almost immediately upon finding the ring, he commits murder of his friend in order to control it. Gollum then spends the rest of his days chasing after it, first with Bilbo Baggins, and then with Frodo.  Using the ring also sends a signal to its original owners, who are continuously searching for it (Ringwraiths).