The Nashville Numbering System was around long before Nashville became known for music. I’ve seen it called by several other names and it is a basic part of music theory. I’ve heard several bluegrass musicians call it this, so I’m following suit here. As a beginning banjo, mandolin, guitar, etc. player, you should be familiar with this concept and how it works in playing music with others.
Whenever we are playing a song, we are (or should be) aware of what chords we are playing. Either we are playing lead by playing a melody, or we are backing up, usually by playing chords. Either way, there is a chord structure to the whole tune that we keep in mind as the song progresses. Those chords can be referred to by their usual letter designation; here is the usual chord progression for the first few measures of Cripple Creek in the key of G, without regard to the length of each chord: G, C, G, D, G.
One thing to notice very quickly here is that most folks play Cripple Creek in the key of A, not G. To play Cripple Creek then, we then have to transpose the chord progression to the key of A. This chord progression now becomes: A, D, A, E, A. Now this example is easy enough to do, but what about transposing something complex?
Musicians have found an easier way to represent chord progressions. Let’s let the root chord (G for the key of G) be a roman numeral I. That C in the key of G is IV, and D is V. If we transpose this into the key of A, then by definition, A is now the root, so it is I instead of G, D is now IV and E is V. The whole chord progression then becomes I, IV, I, V, I. Notice that this is now independent of which key you are in. I is G in the key of G, and I is A in the key of A; likewise for the IV and V chords. BTW, “I, IV, V” is pronounced as the numbers: “one, four, five”.
If you are wondering how this could possibly make your chord-playing life any easier; trust me – as you progress in musical skills there will come a day when you realize that seeing and playing “I IV V” means a lot more to you than seeing “G C D”, and “A D E”, and “B E F#”, and “C# F# G#” and a whole lot of similar things that are all really saying the same thing: simply “I IV V”.