Wolverine frequently boasts that he's "the best there is" at what he does. Often, it's assumed that Logan is referring to fighting or killing. While these skills are certainly some of Wolverine's greatest strengths, his greatest ability actually lies in mentoring others.
Over the years, Wolverine has taken on several different apprentices. Logan has mentored these young mutants, leading them to become more confident and powerful X-Men. The first young mutant to develop a bond with Logan was Kate Pryde. When she first joined the X-Men, Kate was still going by "Kitty", and she was fairly repulsed by Wolverine's gruff demeanor. Everything changed in the Kitty Pryde and Wolverine mini-series by Chris Claremont and Al Milgrom.
When Kitty was brainwashed by Logan's old master, Ogun, Wolverine traveled to Japan to rescue her. Helping Kitty free herself from Ogun's control, Wolverine also trained her to fight. Together, the two X-Men fought and defeated Ogun. This adventure formed a strong father-daughter connection between Logan and Kitty. Moreover, Kitty grew more confident, adopting the codename of Shadowcat. The next young mutant who Wolverine encountered was Jubilee. In Uncanny X-Men #251 by Claremont and Marc Silvestri, the runaway teenager found Wolverine when he was crucified by the Reavers. Jubilee rescued Logan, and they went on the run together. The duo later found Wolverine's fellow X-Man, Psylocke, and Logan taught Jubilee how to be part of a team. Wolverine's mentorship of Jubilee carried on to her joining the X-Men, where the two remained closer than ever. Even after Jubilee became a vampire, in X-Men #2 by Victor Gischler and Paco Medina, Logan donated his healing blood to help her overcome some of her darker urges.
Astonishing X-Men by Joss Whedon and John Cassaday saw Wolverine take another young mutant under his wing. Hisako Ichiki was a student at the Xavier Institute who incidentally accompanied the X-Men on their mission to Breakworld. Arriving on this alien planet, the X-Men split up and Hisako was stuck with Logan. Hisako was naturally scared, as she'd never been on a real mission before, but Wolverine gave her a rousing "tough love" speech. Logan's words inspired Hisako to join the X-Men and adopt the codename "Armor."
It's hard to think of someone who Logan has impacted more greatly than Laura Kinney, initially known as X-23. Laura was cloned from Wolverine's DNA, technically making him her biological father. Although her initial feelings towards Logan were hostile, Laura eventually came around when she enrolled at the Xavier Institute. Wolverine kept a close eye on Laura, making sure she wouldn't become the ruthless killer that he was. Even after letting her join X-Force, Wolverine kicked Laura off the team in X-Men: Second Coming #2 by Craig Kyle, Chris Yost, and Greg Land. While this move confused Laura, Logan clarified by telling X-23 to figure out what she truly wanted in life rather than simply following orders. When Logan died, Laura carried on his legacy by becoming the new Wolverine, a title which she carries to this day.
After mentoring so many individual mutants, Logan took his guidance to a much larger scale in Wolverine and the X-Men #1 by Jason Aaron and Chris Bachalo. Seeing how young mutants were becoming more like soldiers than students, Logan wanted to allow them to be kids again. Wolverine founded the Jean Grey School, where he was the headmaster. Although the Jean Grey School could be fairly dysfunctional at times, Logan still managed to guide many young mutants onto the right path. Currently, Wolverine is not teaching or mentoring young mutants anymore. Yet Logan still shows a fondness for kids. For example, in Wolverine #1 by Benjamin Percy and Adam Kubert, Logan was shown playing hide and go seek with a group of young mutants.
It's this softer side to Wolverine which should be explored more. Of course, Logan is the "muscle" for X-Force, as a formidable fighter, but Wolverine's more paternal instincts add a lot to his character. Krakoa is the perfect environment for Logan to start teaching young mutants. Wolverine could teach fighting classes and impart practical wisdom upon new mutants, along with all of the lessons he's previously taught other young X-Men. Not only does teaching add a new layer of depth to Wolverine, it also shows how far he's grown as a character. Logan started as a hot-headed scrapper who didn't listen to anyone. Eventually, Wolverine matured into a wise teacher, who helped new X-Men grow. Ultimately, Wolverine is the best there is at what he does, and what he does best is mentoring young mutants.