I had to go back and look at the course guide to Fretboard Wizzard, but there’s a quick guide to the Nashville Number system on pages 13 and 14 of the guide. There’s also a more detailed version on wikipedia https://en.wikipedia.org/wiki/Nashville_Number_System
At it’s core, it’s pretty simple. For any given key there are 7 chords in the scale. So you can talk about the chord progression independent of the key.
Let’s say you are in C. So the chords are C Major, D minor, E minor, F Major, G Major, A minor and B diminished. So those are the 1, 2, 3, 4, 5, 6, 7 chords. Some times you’ll see that with roman numbers and with the Majors as upper case and the minors as lower case. Now if you have a song with a 1-4-5-1 progression, that will be C, F, G and back to C. OK. Now let’s say the singer prefers to sing in A. Well it’s still 1-4-5-1. But the key of A is A Bm C# D E F#m g#dim. So 1-4-5-1 is now A-D-E-A.
Learning to think about it, and to hear it as relative changes (going from the I to the V for example) makes learning songs and, picking up on new songs, and adjusting the key to get along with others easier.
At some level it’s an intentional effort to avoid using the absolute chord names and only talk about the relative chord