Classically, the way that music teachers would refer to notes and chords is to assign them a number. For a classically trained musician, C is 1, D is 2, and so forth. This is because the treble clef is naturally centered on the C note -- if you notice, the "squiggle" surrounds the C note. Also for that reason, if you study music in a Latin country, you will probably refer to C as "Do," D as "Re," and so forth. This can make life pretty confusing if you move among different musical traditions, or have to move a song written in one key to accommodate a singer who croons in another.
That's exactly how the Nashville Number System developed -- it is a way to keep musicians on the same page using a little bit of classical theory and modifying it to fit the needs of a multicultural musical tradition. Let's say one person learned to sing "Amazing Grace" at church in the hills of east Tennessee. Let's say another learned to play "Amazing Grace" in church in Memphis. Perhaps they play this song in two completely different keys. What if you wanted the singer and the bass player to go into the studio and record "Amazing Grace" together for a 45 single? You would have to get them on the same page and quickly, since studio time costs so much. So you pick a key and you make that your 1. Following alphabetical order, everything falls into place after that -- your chord progressions would still be the same interval apart. A studio musician could say "Crossroads, key of B," and then simply indicate numbers and everyone in the room would know what he was talking about: B=1, C=2, D=3, and so forth going on up the scale. It is an ingenious adaptation to an idea that was already fairly good. To learn more about the Nashville Number System, click here.