Mentors may award a new user a mentor bonus of 50 reputation. This gives the new user a basic package of privileges, including being able to vote up, comment everywhere, and participate on meta and chat. (It's like the association bonus' younger sibling. The mentor bonus won't count for purposes of awarding that bonus on other sites.)
All mentee activityactivity and responsesresponses are pushed to the mentor's inbox (or perhaps a new indicator on the top bar). That way the seasoned user can monitor the progress of their protege.
Mentors gain special access to some moderator actions over their student's content:
Well, it should be obvious with a bit of digging that the new user was gifted the mentor bonus. (There will even be an entry in the reputation accountingreputation accounting.) And if some 30k+ user suddenly close one of their questions single-handedly, it'll be clear what happened. But the identity of their sponsor should be generally secret to minimize social pressure on them: