When we approach book three, Telemachus makes a journey with the goddess, Athena, who is disguised as Odysseus' old friend Mentor. When they finally reach Pylos, Mentor urges Telemachus to speak with Nestor, a wise Greek warrior, who fought along side his father, Odysseus. Initially, Telemachus is afraid for two reasons.
First, Telemachus is very young and inexperienced with "manly" things. We need to keep in mind that Odysseus traveled to fight in Troy when Telemachus was only an infant. With the passing of ten years, Telemachus is still a teen.
Second, Telemachus believed that this father was dead. It was only at the encouragement of Mentor that he has any hopes at all. Now he is coming face to face with Nestor to learn of this father. This alone must have been nerve racking. After all what if Telemachus found out that his father was dead?