The cunningham is a line that passes from the boom, up through a cringle (reinforced eyelet) set a foot or two above the tack of the sail, and back down to a cleat. Hardening it increases luff tension, which moves the draft (point of maximum curvature) forward in the sail. Named for the famous racer (Briggs) who popularized it, the cunningham works together with the traveler, mainsheet, outhaul and vang to optimize sail shape.
Why use a cunningham rather than simply hoisting the sail higher to add luff tension? Because class racing rules and rigging layout often fix the head position. A cunningham lets you add tension below that fixed point without moving the whole sail up, keeping the head of the sail correctly positioned in the rig.
In light air, ease the cunningham to allow the draft to sit naturally in the middle of the sail, creating a fuller, more powerful shape that captures more wind.
As the wind rises, and before reefing, harden up the cunningham to depower the main, move the center of effort forward and reduce weather helm.
On racing boats, skippers might adjust the cunningham continually as wind force and direction change during the race.