There is no certain theory that explains the reason behind Naruto’s whiskers. However, there are a few theories that appear in most possible cases.
One theory states that Naruto is the son of a jinchuriki named Kushina. Kushina was the jinchuriki of the tailed fox, Kurama. The fox has whiskers on his face and this proves that somehow one of Kurama’s traits was passed to Naruto when he was still in his mother’s womb.
Another theory states that Naruto itself is a jinchuriki of the Kurama. Because of that reason, Naruto has the same whiskers as Fox. However this theory is not valid as Minato sealed Kurama within Naruto when Obito (mask guy) attacked Konoha, but Naruto had whiskers before that as shown in the anime.
Another possible reason could be that, Masashi Kishimoto has designed Naruto with whiskers because he wanted him to appear that way and to raise questions about his appearance which ultimately makes people more involved towards the character and anime.
So as it is an open-ended matter, you can add your possible interpretation too. Any of the above-mentioned theories could be the real case.