What's the point of Mentes' reference to Prince Orestes in line 343 of The Odyssey by Homer?
After Athena (in the form of Mentes/Mentor) has time to visit with Telemachus in Book 1 of Homer's The Odyssey, she is able to begin building his confidence. The young man is feeling bitter that his father left to help another family, leaving his own family to be plagued by suitors who are eating away (literally) Telemachus's inheritance. In short, Telemachus is resentful and bitter, but he does not feel as if there is anything he can do to change things.
Athena attempts to empower the young man by talking to him (still in disguise) about what the great Odysseus would do if he were to arrive home and find the suitors wreaking havoc on his home and his family.
Another way she tries to motivate Telemachus is to remind him about Orestes, the son of Agamemnon who killed his own mother and her lover to avenge his father's death. She says:
"You must not cling to your boyhood any longer--it's time you were a man. Haven't you heard what glory Prince Orestes won throughout the world when he killed that cunning, murderous Aegisthus, who'd killed his famous father?"
Of course what Athena is hoping to do is inspire Telemachus to take some action by reminding him about another son who took action and acted like a man to do what was (arguably) right. That is the point of Athena talking to Telemachus about Orestes.
This allusion to Orestes comes from the Greek Tragic play The Oresteia. Orestes kills his mother, Clytemnestra, and her lover, Aegisthus, after they have murdered his father Agamemnon upon his homecoming from the Trojan War. Odysseus, like Agamemnon, is trying to return home after his victory at Troy, and his household has also been overturned during his abscence. Athena is reminding Telemachus of the tragic consequences of a past Greek war hero whose victories were nothing because his wife and other family members failed to remain loyal to him. She is inspiring Telemachus to protect his household so that Odysseus does not suffer the same fate.
Furthermore, Athena supports Orestes at the end of the Orestia,so he is not punished by the vengence and desire for justice of other Greek gods. Not only can Telemachus win glory as Orestes did, but he will also be supported by Athena in his efforts.