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The piece is Chopin's waltz in A minor op. 34 no. 2, measure 70:
We seem to be in the key of A minor due to the cadences in measures 71 and 73. But B-flat major is not in the key of A minor (right?). Is there a concept in music theory that explains this or is it just an irregularity? I must be missing something.
This is a very common concept known as the Neapolitan chord.
In short, the Neapolitan chord is typically a major chord built on the lowered second scale degree; you'll occasionally see/hear it called the ♭II. It's also commonly in first inversion, so you'll also occasionally hear it called the "Neapolitan six(th)," the "six" indicating the figured bass for a first-inversion chord. The Neapolitan chord functions as a predominant, often moving to V immediately afterwards (as it does in this example).
In the A minor of this example, scale-degree 2 is normally B♮, but lowering it one half step gives us B♭, the Neapolitan scale degree.
The "Neapolitan chord" answer deserves to be the accepted answer, but I'd like to add another use for Bb in Amin.
The bII can be used as a tritone substitution for the V, and particularly the V7. In Amin, for example, E7 resolves to Amin (or Amaj, but here Amin) basically because E7 has G# and D, but Bb7 also has Ab and D (assuming G# and Ab are the same note on your instrument), so you can resolve Bb7 to Amin. This is much more common in jazz than in music of Chopin's era, so I'm sure that's not what Chopin is doing in your example, but it's sometimes the right answer to the title of the question.
The chord sequence C - Bb - F (or variations on it) is common in modal music where the scale more often uses the minor 7th. It's also a frequent element of rock music, for example in the song Can't get enough of your love.
The relative major/minor relationship between C major and A minor should be clear, of course.
In addition to the other answers, there is a more general concept of full tone and semitone chord movement in chord changes in general. This is frequently employed as a major triad or one of its inversions. Often, the bass note sometimes is and sometimes is not a part of the harmonic triad. You also often see the inverse of this, where only the base note moves in full tone or semitone steps while the harmony sticks to the primary chords of the key with a more pedestrian chord progression (e.g., ii-V-I or vi-ii-V-I). This happens a lot in jazz but you also see it in rock, pop and classical.
I'm not sure of any theoretical basis for this other than that it's really just progressive movement along the chromatic scale in the case of semitone movement and the diatonic scale in the case of full tone movement.
From a compositional perspective, it's a relatively simple matter to just try a semitonal or full tone chord change within the context of the song you are writing and just "see" if it "works" in the context of whatever song you happen to be composing.
