What’s the Point of “Neapolitan Chords”?

Firstly, simply put, it’s worth giving names to things that frequently appear in specific forms (contexts). This is especially true for the sake of convenience in analysis.
For example, in jazz, you might call the IVm-♭VII7 motion a “backdoor ii-V“, which is simply a type of modal interchange. The “Coltrane Change” and “So What voicing” are similar cases.
The Neapolitan chord is a famous chord frequently found in classical music especially in the 18th century, also appearing in works by composers like Chopin and Beethoven. So it naturally deserves a name given its recurrent use as a prominent harmonic device.

Musically, the Neapolitan chord can be interpreted as a modal interchange, but is unique in two respects:

1)Typically played in its first inversion. In the key of Am, for instance, it would be B♭/D. The fact that it’s not just B♭ is crucial. (And this form is particularly called a “Neapolitan Sixth”.)
2)Placed before the dominant chord in a minor key. In the key of Am, it forms progressions like B♭/D→E7 or B♭/D→Am/E→E.

Thus, it is characteristic that it is utilized as a substitute for Dm, the minor subdominant, due to the bass being D.
You can rarely find other non-diatonic chords that is typically used in inversion. The Neapolitan sixth chord stands out in this regard.

Johnny :

On improvisation, what scales do you play on this chord?

Let say in C minor key, Neapolitan Sixth is D♭/F. Since D is flattened, one candidate is definitely Phrygian. Alternatively, you may raise the 7th from it to make the leading tone like the harmonic minor manner, which is called a “Neapolitan Minor” scale.