The first four books of Homer's Odyssey are sometimes called the Telemachia, because they deal with Telemachus' efforts to find news about his his father. One reason Athena helps Telemachus is because she is a goddess of war and wisdom. As such, Athena is a divinity well suited to provide a young man like Telemachus with the courage and confidence he needs to undertake his own personal quest for his father.
Another reason Athena helps Telemachus is because of his father. Athena favored the Greek side in the Trojan War and since Odysseus fought for the Greeks, Athena was likely to be favorable to Odysseus and his family.
From a practical, religious standpoint, Athena is willing to help Odysseus and his family because he has sacrificed habitually and frequently to the gods. When Athena reminds Zeus of this in Book 1, the king of the gods responds:
How could I ever forget godlike Odysseus, who exceeds all mortals in wisdom, and also in sacrifice to the deathless gods who inhabit the broad heavens? (A.S. Kline translation)
Thus, the reasons why Athena helps Telemachus are partly because of the relationship she has with his father and partly because she is the divinity most commonly found helping Greek heroes.