Hi!
Can someone explain what this is and how to use it
Maybe @BassCliff will post a pic of one of his music sheets.
There are lots of resources online that talk about and explain the Nashville Number System. In a nutshell, The NNS is based on the triads built on scale tones. Using the numbers is a kind of shorthand musical notation. There are also other symbols used to designate breaks, holds, pushes, etc.
If I say "This song is 1-4-5 in the key of A" what I'm saying is the chords are build on the first, fourth, and fifth notes in the scale of A. In other words, the chords are A major, D major, and E major because the A scale is A, B, C#, D, E, F#, and G#.
As @tshapiro mentioned earlier the 1, 4, and 5 chords are major triads. The 2, 3, and 6 chords are minor triads. The 7 chord is a diminished triad. However, I have fount that, especially in country music, the chords that are normally minor or diminished might not actually be so in a particular song. Sometimes a dash or a superscript 'm' used behind a number will signify an actual minor chord...
But I've found that there are a several variations and short cuts used by different musicians. Here is a Nashville Number Chart actually used in a Nashville studio by Nashville musicians for a song written by a Nashville cat.
Each number represents one measure. IF there is a line under two or more numbers, they are all part of the same masure. The > symbol means the chord is "pushed", i.e. played on the upbeat (the eighth note before the beat). You also see some rhythmic notation written as notes above the number chords.
When I write a number chart I tend to use staff paper incorporate a little more actual musical notation. Here's one of mine, a Garth Brooks song that we cover.
My chart says "Long bars" while Jed's chart says "Fast bars". This means you count my chart in half time. Each bar is actually eight beats. That's why some of the rhythmic patters don't add up. It's just enough to keep me true to the recording.
The really cool thing about number charts is that you can play them in any key, transposing instantly. If the singer needs to go up or down a whole step or a fourth, it doesn't matter. You can still use a number chart and play the song in the new key, just change the tonic (the first note of the scale of the key you're in).
There ya go. Clear as mud, right?

Here's an intro by Chas Williams who wrote a pretty concise book about the NNS.
This is a bit technical but tells you about how the scale notes (numbers) relate to the chords built on them:
The Nashville Number System Simply Explained - How Music Really Works
Thank you for your indulgence,
BassCliff