This scene shows us two things that are very important to the story. First of all, it shows that Penelope is faithful to her husband. She does not want the suitors there in her house. She does not encourage them in any way. She tries her best to be "proper" in the way that she appears to them and how she behaves towards them. This is important so that Odysseus knows that she has been faithfully waiting for him. He needs that encouragement to fight off all of the younger, angry suitors.
The second part to that is that he gives her hope. He tells her that Odysseus is on his way home. He gives her proof that he has seen him by describing several items that he wore and things that he carried with him--to prove that Odysseus is out there waiting to return. This hope he gives her helps her morale as well.