“Smells Like Teen Spirit” uses four chords from F natural minor: i (F minor), iv (B-flat minor), ♭III (A-flat), and ♭VI (D-flat). The Roman numerals refer to the scale degree that the chord is based on. F is the first note in F natural minor, B-flat is the fourth note, A-flat is the third note, and D-flat is the sixth note. The left diagram below shows F natural minor on the chromatic circle. The right diagram shows it on the circle of fifths. The blue arrows follow the chord progression.
The chord symbols say F5, B♭5, A♭5 and D♭5 because they’re power chords, meaning they have no thirds, just roots and fifths. (If you play “Smells Like Teen Spirit” with full chords rather than power chords, it sounds good, but the effect is more gentle and less aggressive.) A song based on power chords is a series of parallel fifths, which are against the rules of classical counterpoint. In rock and roll, however, parallel fifths are perfectly fine.
Right before the A♭5 chord, there’s a brief G5. The G is the second note in F natural minor. The other note in G5 is D, which is not part of F natural minor at all. The G5 is just there to slide up to A♭5. Anticipating a chord with the one a half-step lower is common practice for guitarists.
“Smells Like Teen Spirit” is full of nifty symmetries. Think of it as two pairs of chords: F5 and B♭5, and A♭5 and D♭5. (I’m ignoring G5 because it’s more of an embellishment.) If you use full chords, the pairs are F minor and B-flat minor, and A-flat and D-flat. Each pair is a fourth apart. B-flat is the subdominant in the key of F minor, and D-flat is the subdominant in the key of A-flat. The two pairs are separated by a minor third. F-minor is the relative minor chord of A-flat, and B-flat minor is the relative minor chord of D-flat.
There’s nice parallelism to the rhythm, too. In the front half of each bar, the accent is on beat one. In the back half of each bar, the accent is an eighth note after beat three. The stable-feeling F minor and A-flat chords fall on strong beats, while the less stable B-flat minor and D-flat chords fall on weak beats. It’s a whole composition lesson in two bars.