The explanation that I've always heard for this has to do with induced drag and wingtip vortices. Of course, this explanation is simplified and in layman's terms only.
It works like this: If you imagine a wing with infinitely long wings, then lift is created on such a wing by the air across the top having a lower pressure than the air across the bottom. People argue about "bernoulli" lift, vs. "newtonian" lift, but it all basically boils down to that simple statement. The air across the bottom as higher pressure than the air across the top. The higher pressure on the bottom surface pushes the wing UP more than the lower pressure on the top surface pushes the wing down, and VOILA-- Lift!
In an infinite wing, there are no wingtips- because the wing goes on forever. Obviously such a wing can only exist in theory, but it's useful for doing the mathematics. Anyways, in an infinite wing once the air hits the wing, the air that travels along the bottom can't get to the top, and vice versa. In a "real" wing, however, (which doesn't have infinite length) near the wing tip some of the air on the bottom tries to move around the side of the wing due to the higher pressure on the bottom of the wing than the top. This "spilling over" is what produces wing tip vortices. And these wing tip vortices are BAD. The reduce lift and increase drag.
Anyways, the airflow pattern around the wing depends on the shape and SIZE of the wing. This pattern includes the vortex pattern at the tips of the wings. That vortex pattern is also proportional to the size of the wing (and other things, too).
It turns out that when the wing is about 1 wingspan above the ground, that vortex pattern starts to hit the ground in it's attempt to go from the bottom of the wing to the top of the wing. This starts to break up the wing-tip vortex a little bit, and prevent some of that loss of lift and increase in drag. This is what we call "ground effect"
Anyway, I've heard ground effect described as beginning 1 wingspan in altitude, and I've also heard people say that it's 1/2 wingspan in altitude. Probably a question of how much of an effect there has to be before people say that it's a "SIGNIFICANT" effect.