In a recent interview from Playstation.blog, director of Final Fantasy XIV: A Realm Reborn Naoki Yoshida explains this new feature in Patch 3.2 designed to enhance the experience that newcomers have with this MMO's community. Students of the mentor program qualify if their playtime is less than 40 hours. Experience points bonuses are awarded to both the new mentor and the student when they form a party together. Additional bonuses will be awarded to the mentor for their participation, so that's another plus.
The idea behind the concept is to develop the community of Final Fantasy XIV by also making it a mutually beneficial deal for veterans and rookies. I’ve had a couple friends ask me time and again if I’ll ever give FFXIV a shot and maybe now I’ve run out of my last excuse.
Yoshida offers up tons more details in this interview including the listed requirements to qualify as a mentor.