Love the Clapton comparison
But, the aft ring is for a flattening reef, not a cunningham.
As you say, the purpose of the cunningham is to increase (or decrease) luff tension in the lower part of the sail, which in turn moves the deepest part of the camber (point of max depth) forward (with tension), or aft (by easing tension if any).
It does the same thing as increasing or decreasing halyard tension, but whereas you get more effect from halyard adjustments in the upper section of a sail, the cunningham affects the lower portion.
The flattening reef is like a turbocharged outhaul; as you add tension here on the mainsail leech, you REMOVE draft (rather than MOVE it as with a cunningham), thus flattening the sail, or making it fuler when you ease tension on it. It will have the effect of reducing heeling as Frank says and in the right conditions be faster, since less heel is almost always much faster.
They are not used much anymore since mainsail shapes have evolved to be flatter to begin with, and you can achieve what you need simply by adjusting the outhaul, but this is what that ring was for..
Cheers,
S