Basically, Athena made him bigger, stronger, almost god-like in appearance. She is really only mentioned briefly in the beginning of Book 2. As Telemachus enters the assembly ground
"Athena lavished on him a sunlit grace that held the eye of the multitude. Old men made way for him as he took his father's chair."
With both his magical appearance and his gifted speech (which he inherited from his father), Telemachus is able to impress the men of Ithaca. and hold their attention until Antinoos speaks up and challenges him.
The importance of Athena helping Telemachus relates to her feelings towards Odysseus. Athena holds Odysseus close to her heart (for a goddess). She is the goddess of war and wisdom, and Odysseus is a true warrior and a wise one at that. He personifies what she stands for, and it is said that she loves him because of this bond. She does what she can by altering Telemachus' appearance and helping him to travel for news of his father.