In Book 2, Telemachus has come before the assembly to complain about the men who are hanging around his house trying to woo his mother. The suitors argue that it is Penelope's fault that they are still hanging around. If she would just get serious about accepting one of them, the rest would leave.
During the assembly, Halitherses gets up and makes a prediction. He is a prophet, so it makes sense that he would predict things. He predicts that the suitors are going to be in big trouble because Odysseus is going to return home and he is going to be very angry.
Halitherses, the son of Mastor, is an Ithacan prophet. He was a dear friend of Odysseus', along with Mentor. He is one of the people who remain loyal to Odysseus even after his long absence. When the suitors first come, he attempts to stop them but is unsuccessful.
In Book 2, he warns the suitors that they are ill-fated. Zeus has sent him some symbols of what will eventually happen. Because Halitherses is an augur (a special kind of prophet who interprets prophecies from birds), the symbols come in the form of two vicious, fighting eagles. When Odysseus finally comes home to Ithaca, they will all be punished severely. He tells them that if they are "wise in time" and stop pursuing Penelope so wickedly, they will survive. However, if they don't before Odysseus arrices, they will all die. None of the suitors listen to him.
Later in the epic, after the suitors are all dead, Halitherses gives another warning. He tells the families of the suitors not to take revenge, or more bad things will happen. Half of them listen, but the other half try to get revenge on Odysseus and Telemachus. Athena swiftly destroys them all, just as Halitherses predicted.