In X-Men: Evolution, most of the classic mutant heroes and villains of the Marvel Universe are re-imagined as teenagers either aligned with or against the Xavier Institute -- splitting their time between their secret identities at the Bayville High School and their mutant personas, and these young X-Men train under the guidance of Charles Xavier, Storm, and Wolverine. These three (along with Beast, who is introduced in the show's second season) remain adults in this adaptation and become more crucial as mentors rather than drive the primary plot lines of the show themselves. While this was something of a mixed bag in terms of results, it turned out to be an ideal approach to Wolverine.
Within the context of X-Men: Evolution, Wolverine was an early student of Charles Xavier. Found sometime before the events of the series, Logan is already far removed from his feral past by the time the show introduces him. Although elements of his past continue to haunt him through the series, Wolverine is content to serve as a mentor to the young X-Men who are decades his juniors. Over the course of the show's four-season run, Logan becomes increasingly close with some members of the team and shifts more and more into the role of teacher to the New Mutants, who follow the original batch of students. His greatest challenge arrives in the form of X-23, his clone -- whose debut in the series saw her and Logan come to terms with each other and cement Wolverine's development into a mature and dependable mentor.
In other adaptations of the X-Men -- most notably the live-action X-Men films by 20th Century Fox -- Logan can easily become the center of attention, but by keeping Wolverine separated from the central storyline, the show was able to properly focus and develop its core cast of Cyclops, Jean Grey, Nightcrawler, Shadowcat, Spyke and Rogue. Wolverine being aged down like the rest of the cast would also have cost him much of the mystery and wild history associated with the character, something the show utilized well in the episodes that did focus on him. Plus, making him a teenager would have added an uncomfortable layer to his torturous experimentation under Weapon X that the all-audiences series was likely never going to tackle.
Making Wolverine into a mentor figure makes sense as a way to keep him in the show but at enough of a distance that he didn't overwhelm the rest of it. It's also a strong development that also works within the context of the character and how he's presented in the show -- and is a fairly accurate representation of the character's growth in the original comics.
In series like Uncanny X-Men, Logan went through a similar arc with generations of characters -- becoming a surrogate father or brother figure to plenty of young mutants (including Shadowcat, Jubilee, Armor and Quentin Quire). That commitment to protecting younger and more troubled heroes continues into the Krakoa era, with his motivation becoming focused on protecting generations of other mutants while he stands the test of time and threat.
X-Men: Evolution highlights a side of Wolverine that is rarely seen outside of comics, the formerly violent and isolated warrior turned into an honorable and dependable teacher. It doesn't erase those elements, but treats them as part of his backstory instead of the show's actual story. This helps keep the focus on the X-Men themselves, and not just him. Being a teacher is also such a core element of Wolverine's growth in the comics that he spent years as the head of his own school -- so it's good to actually see it reflected in this version of the character. X-Men: Evolution found a way to turn Wolverine's comics growth into their version of Logan's arc -- in a way that helped the rest of the cast and feels especially refreshing after other adaptions focused primarily on his mysterious past and his feral nature.