Neopolitan What?

I had seen the Neopolitan Sixth (N6) in various music theory books and online posts, but always glossed over it because to me it's name implied some esoteric flavor I'd have little use for (like Neopolitan ice cream, a mash-up of what I experience as three unrelated flavors).

Regardless of it's fancy name (never mind where the 6 in the name comes from), it's nothing more than a bIIMaj7.  As long as the I for the key has been established in the listener's ear, it will resolve back to the I which can be either major or minor.  This is what the GbMaj7 is doing in "The Girl From Ipanema".  It's just a more subtle way of getting back to the home key, F.

To make the N6 (bII7) a little easier to understand, imagine it were a dominant 7 instead of Maj 7.  In other words, imagine that GbMaj7 was written as Gb7.  In the key of F, Gb7 is a tritone sub for C7 (b5). 

When written and played as a major-7 chord, we can note that Dbmaj7 is enharmonic to F- with a b6 in the base. This might be the motivation for the name "Neopolitan 6".  When soloing over it, we might think of it as a variation of a minor-iv chord. That happens often enough that we should already know what to do.