Mentoring is a new interaction in The Sims 4. When a Sim maxes out a skill at level 10, they can then mentor other Sims in that skill. When a Sim is being mentored, they develop that skill quicker than without the help of a mentor. Mentoring also helps improve friendly relationships between Sims.
Mentoring is a way of sharing expertise to help other Sims develop skills.
In order to mentor a Sim, that Sim must be working on the skill at that time. For example, a Sim who is at level 10 in Fitness goes into a gym. She sees other Sims working out—thus they are working on the Fitness skill. She can walk over to the Sims, and after introducing herself to them if she does not already know them, offer to mentor them. The mentor social becomes available if the above conditions are right. If the Sim is just standing in the gym talking to other Sims, the mentor social will not be available. So while the mentor is helping the learner, the learner is gaining the Fitness skill at a faster pace than normal.
Mentoring is very effective when using it with Sims in the same household. You can get one Sim started on a skill, then take control of the expert Sim and begin mentoring.