As you know, most soles are flat at the waist. The bottom of the sole is simply a flat piece of leather running from toebox to heel. With a fiddleback waist, the waist area is shaped. The sole is substantially thicker in the middle and then thins toward the edges, giving it a shape similar to a stretched-out U. Essentially, it appears convex when viewed from the side. This is accompanied by a narrow waist, making the sole look like a violin or fiddle.
Fiddlebacks usually go hand-in-hand with a beveled waist, though it's possible for a shoe to have a bevelled waist and yet not be a fiddleback.