The "button" simply activates the clipping mechanism on the backside of the controller; it has no gameplay/interactive value (i.e. the Wii doesn't register that the button is pressed, it's simply mechanical).
However, the question does remain of what it's meant to clip the Virtual Controller to. Some speculate that it's "left over" from when it was going to be a "shell" instead of connected via cable; however, this is not accurate as in no point in the development cycle was it a clip-on product, it was originallly going to be a shell, then they went with the cord (which I prefer).
The most plausable theory is that it is for use to be attached to a rumble pack that may be released in the future. It really is a mystery, though, as it's just a physical clip - there is no data recepticle.
Wii will see...