The NNS system is a way of notating and understanding music using numbers and intervals (distance between notes) instead of our traditional musical alphabet. It was made famous by Nashville studio musicians whose "back-to-back" studio sessions made it challenging to memorize a dozen or so songs EVERY day; they needed a better way! Necessity is the mother of invention, and so the Nashville Number System was born! This shorthand method of notation and understanding allowed the seasoned musician to perform songs "off the cuff" having never heard the song before, saving musicians time and energy.
For me and the many musicians who have embraced this method of musical understanding, it's become the most important tool in our arsenal. It's the "magic" behind fretboard memorization and knowing what, when, and where to play. Once you see music from this new perspective, you'll wonder how you ever got along without it.