The following explanation and pictures were taken from
here - scroll for "Gybing heads".
Gybing Heads Some boats use what is known as a "gybing head" design. If you look at the following picture, you can see that the head is trapezoidal in cross section, rather than the more typical rectangular.
What this does is allow the centerboard to pivot inside the centerboard trunk (rotating about the point of maximum thickness of the head). The forces causing the board to pivot are (1) the lift being generated by the foil, and (2) the lateral resistance from the foil preventing the boat from slipping sideways through the water. Usually you can view the lift vector as being concentrated at the 25 % chord, while the lateral resistance is more or less evenly distributed across the foil. If the pivot point is greater than 50% back from the leading edge of the foil, then the forces will cause the centerboard to be pressed against the side of the trunk, and it is "gybed" into position. Typical centerboard gybing angles are about 3 degrees. The centerboard only gybes when it is all the way down - as soon as you start to rake it back in the trunk, the fat leading edge of the foil will jam enter the trunk and cause the centerboard to jam in a straight fore-aft position.
Why do you want a gybing centerboard? By the board rotating to windward, you increase the angle of attack of the centerboard with respect to the centerline of the hull, and therefore generate more lift, all else being equal. In practice this means you can steer the boat slightly lower and sail with a fuller jib for increased power while maintaining the same leeway angle as a similar boat with a non-gybing board. That's the theory - some fleets like them, some don't (and many one-design classes don't allow them). Frank Bethwaite in "High Performance Sailing" claims they are a bad idea as the rudder may end up directly in the disrupted flow from the centerboard.
Click
here for a short overview of the fabrication process.