A Neapolitan 6th chord belongs to the pre-dominant family, and is therefore used to approach the dominant chord in a key. More specifically a Neapolitan 6th chord is a major chord built on the lowered 2nd scale degree, and placed in first inversion.
For example, in the key of C major the 2nd scale degree is D, so a Neapolitan 6th would be a D-flat major chord (as D-flat would be the 2nd scale degree lowered by a half-step) in first inversion, so spelled from the bass up: F-A-Db (though, to be perfectly clear as long as the F is in the bass it doesn't really matter what order the other two pitches are in, as long as they are there. F-Db-A would be just as good).
Voice-leading would then usually have the flatted 2nd scale degree go to the leading tone (NOT tonic yet), while the F would move to the dominant. The dominant harmony would then be resolved as usual with the leading tone moving up to tonic and the 5th scale degree leaping down to tonic in contrary motion. Other resolutions do exist, however, depending if a cadential 6/4 is used.