The I, IV, and V chords for any given key are connected by the lines here. Although it's a little misleading. For example, the key of D major the I, IV, and V are D, A, and G (all major). You can see that D is connected by these lines to A and G. But this connection sort of looks like you would start on D and D, G and C. When in fact it's D, A, G. So you would change this to be closed isosceles triangles between the DAG to we that more clearly.
However the DGC connect does show perfect fifths. In fact, you can easily derive the circle of fifths from this picture by starting on B, beadgcf.
This image shows the order of the notes, the circle of 5ths and the I,IV, V (if you look at it the right way).
There's probably a lot more hidden on here. It's just counting by 4s or 5s or 3s repeated.
There is another way of drawing this where you get perfect 4ths and 4 cool overlapping triangles, but it's not as meaningful.
Finally if you use the top and number it 0 and go to 11, you can use clock math to know all the notes on a fretboard. For example, A is 0, F is 8, so the 8th fret of the A string will be F.