A mentor is a victor of a past Hunger Games who must train subsequent tributes from their district. There are no gender restraints; a male victor can train a female tribute and vice versa. There can be 2 male mentors or 2 female mentors, though usually there is one female and one male. Haymitch Abernathy was Katniss Everdeen and Peeta Mellark's mentor in both the 74th and 75th Hunger Games. Katniss and Peeta only had one mentor because Haymitch was the last living victor of District 12.
Though victors are not required to either go to school nor work in their district's industry, they are required to work as mentors who train their District's tributes that follow after them for the rest of their lives.
Mentors prepare their tributes for life in the arena, give them tips on strategy, and help prepare them for their public interview with Caesar Flickerman. A mentor is also crucial in helping procure sponsors for their tributes as well as having the power over the gifts that go into the arena for their tributes and when they are sent in.
Each mentor lives in the Victors' Village, a small part of every district that is made especially for the victors of the Hunger Games. The houses are luxurious and filled with goodies that the rest of the district's citizens do not have.
These are not confirmed but are presumed, especially in the career districts where there are more victors.