Very simple really. A conventional tail-plane has a fixed surface, with elevators at the trailing edge which move up and down in response to pilot commands, thus changine the angle of attack of the surface as a whole. In an all-flying plane, there is no fixed part - the pilot alters the angle of attack by moving the whole surface. The PA28 is a very common example, so you can probably go down to your local airfield to see it in action - just move the tail-plane up/down, and notice that the whole thing moves, instead of just the back part.
The advantage of this setup is that it gives a very powerful control surface. Usually, it turns out to be too powerful, and the control forces required to move it in flight are too light, so they are often fitted with an anti-balance tab to increase the amount of force required to move it.
Hope that helps.
FFF
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