Naruto Uzumaki has a pretty recognizable design. He has a headband with a leaf symbol, a bright, orange jumpsuit with a red spiral on the back, and Zōri sandals. However, his most distinguishing characteristic would have to be the whisker-like markings on either side of his face.
As cool as Naruto's whiskers are, there's a mystery as to how they got there. There are no official sources that explain them, so fans are left to speculate on the matter. The obvious answer is that they're a cool and unique design, but perhaps there can also be a good, in-universe explanation for their existence.
The first and simplest answer for Naruto's whiskers is that they're a design choice. Masashi Kishimoto wanted Naruto to look like a fox who had taken human form. This much is implied by the original pilot for Naruto where the boy's true form is a fox. It's also suggested by Ebisu in the early chapters that Naruto is the Nine-Tailed Fox's human form, though later chapters would suggest that this is metaphorical at best. Regardless, the initial concept of Naruto being a fox, whether literal or figurative, is readily apparent.
As for why the whiskers appear as black lines, that's a result of Naruto's original medium-- manga. In a format that's primarily drawn in black and white, black lines are the best way to portray what would probably be relatively subtle markings in real life. An alternative might be to shade Naruto's skin and then add white lines on his cheeks, but that would be much more effort than is necessary.
The whiskers may just be a creative choice, but not all fans are satisfied with such an answer, so they look for clues within the narrative. For example, the whiskers seem like a distinctive trait, but they aren't exclusive to Naruto. They also appear on Ginkaku and Kinkaku, who gained some of the Nine-Tails' chakra by eating its flesh. This could mean that the markings are exclusive to those with a connection to Kurama.
This theory about the whiskers is further backed by how the whiskers' appearance changes when the Nine-Tails' chakra is used. When Naruto first uses it, his whiskers cover more of his cheeks and become more pronounced. When he achieves higher levels of his Nine-Tails Chakra Mode, explicit markings appear on his face over his whiskers. These changes seem to further indicate that the whiskers are an influence of the Nine-Tails.
As likely as it sounds that Kurama gives people whiskers, there are a few points to debate in the theory. The first is that Naruto was apparently born with his whiskers before the Fox was ever put into him. Secondly, Naruto's mother Kushina was once a Nine-Tails jinchuriki, yet her face is free of markings. Furthermore, Naruto's children have whisker patterns on their faces despite never directly receiving chakra from Kurama. These could all be written off as oversights on Kishimoto's part, but if they aren't, then there has to be another reason for the whiskers.
It's possible that Naruto's whiskers are some sort of birthmark. This covers the potential oversight that he got his whiskers before being imbued with Kurama's chakra. Granted, the shape and placement would be a little contrived, but birthmarks come in enough shapes, sizes, and even colors to grant this theory leeway.
Another possibility is that the markings come about while in the womb of someone with Kurama's chakra. This qualifies both Naruto and his children to have whiskers. Hinata isn't a jinchuriki, but she did have Fox chakra imbued in her during the Fourth Great Ninja War, so some residual chakra may have influenced Boruto and Himawari. However, this still doesn't account for Kinkaku and Ginkaku, so it's also debatable.
Whatever the reason, the fact is that Naruto's whiskers have no definite reason for existing. Neither the manga nor Kishimoto have elaborated on how they got there. It's up to the fans to draw their own conclusions on the matter.
