A mentor is a concerned counselor
When Odysseus, hero of Homer's epic poem the Odyssey, set out for the siege of Troy, he was afraid that he was going to be gone for quite some time; so, he left his household and his wife, Penelope, in the care of his trusted friend, Mentor.
When Odysseus was gone, things went from bad to worse in his house because of Penelope's suitors drinking up the contents of the wine-cellar and butchering the cattle for their own use.
The wise goddess, Pallas Athene, saw what was going on from the Olympian heaven, and became concerned that Odysseus wouldn't have any home to come back to; so, she asked Zeus, the father of the gods, whether she shouldn't go down and help out.
He agreed that she should; so, Athene assumed the shape of Mentor and whispered a great deal of sound advice into the ear of young Telemachus, son of Odysseus. As a result, even to this day, a mentor is considered to be a wise counselor.
More Information about the History of the Term Mentor
Mentor has become a well-known word that is used in the professional, educational, and other areas where it is considered to be a good idea to have a mentor, a trusted and knowledgeable counselor, who can give another person the best guidance for a successful career or future life.
François Fénelon (6 August 1651–7 January 1715), was a French Roman Catholic archbishop, theologian, poet and writer in his The adventures of Telemachus, first published in 1699, emphasized Mentor as a character and so it was that in French (1749) and English (1750) the term mentor became a common noun meaning 'wise counselor'."
"Mentor has become acceptable for such a person because it means "adviser" in Greek and comes from the Indo-European root men-, mon-, meaning "to think".
You may see more information about menti- words located at this link.