I came to this discussion from another thread. I am not into this lesson yet, but I think that I can provide a different way to answer to the first post of the discussion by Paul @guitar82. I hope it can be helpful to someone.
Edit: where appropriate, as Shane @sclay sensibly suggested, the chord diagrams shown below are now the minor versions to make easier to spot in the minor pattern, not only the root or tonic notes of the chord, but also the minor thirds of the chord. Cmin (Amin shape) and Gmin (Emin shape) are usually played as barred chords so there is no direct comparison; therefore, I kept the major version.
A CAGED E Shape has the root or tonic notes of the scale (the ones that give name to the scale) in the same relative position of the E major or minor open chords (6th and 1st strings, and 4th string two frets up the neck):
A CAGED D Shape has the root or tonic notes of the scale in the same relative position of the D major or minor open chords (4th string and 2nd string three frets up the neck):
A CAGED C Shape has the root or tonic notes of the scale in the same relative position of the C major open chord (2nd string and 5th string two frets up the neck):
A CAGED A Shape has the root or tonic notes of the scale in the same relative position of the A major or minor open chords (5th string and third string two frets up the neck):
A CAGED G Shape has the root or tonic notes of the scale in the same relative position of the G major open chord (3rd string, and sixth and first strings three frets up the neck):
As far as I know this applies to any scale; all scales has a root or tonic that is the first note. As Chris @jacksprat and Tom @Tbushell show in their posts, the patterns facilitate to play notes of a scale in different parts of the neck. For example in my Level 9 practice I am practicing the A minor pentatonic scale using Pattern 1 on the 5th fret. If I want to play the same scale one step closer to the nut I need a pattern that has the root or tonic in the 6th and 1st string so I would need Pattern 5 on the second fret. If I want to play the same scale one step closer to the bridge I need a pattern that has the root or tonic in the fourth string so I would I need Pattern 2 on the 7th fret. CAGED system and the patterns are mnemonic devices. How the patterns match the scales is musical theory. How the same scale sounds different if played in different parts of the neck is music.