In the following image we show the i - iio6 - V - i chords in the key of A minor. By lowering the chord's root by half-step (in this case the B becomes a B flat) we get a Neapolitan Sixth chord. It receives the name sixth because it is commonly used in first inversion.
In traditional harmony, chords in first inversion are sometimes called sixth chords. By lowering the root note, we increase the harmonic tension, strengthen its subdominant function and its resolution to the dominant chord. The lowered note descends a diminished 3rd to the 3rd of the dominant chord. Listen to both examples:
Very often the Neapolitan Sixth chord is followed by the tonic chord in 2nd inversion before the dominant chord.