These are among the most ephemeral phenomena that observers see during the few minutes before a total solar eclipse. They appear as a multitude of faint bands that pass over every observer and can be seen by placing a white sheet of paper several feet square on the ground .They look like ripples of sunshine at the bottom of a pool, and their visibility varies from eclipse to eclipse. 19th century observers interpreted them as interference fringes caused by some kind of diffraction phenomenon. The sun, however, is hardly a 'point source' and the patterns are more random than you might expect from diffraction effects.
The simplist explanation is that they arise from atmospheric turbulence. When light rays pass through eddies in the atmosphere, they get refracted. Unresolved distant sources simply 'twinkle', but for nearby large objects, the incoming light can get split into interfering bundles that recombine on the ground to give mottled patterns of light and dark bands, or portions of bands. Near tolality, the image of the sun is only a thin crescent a few arcseconds wide, which is about the same size as the atmospheric eddies as seen from the ground. Bands are produced because the sun's image is longer in one direction than another. The bands move, not at the rate you would expect for the eclipse but at a speed determined by the motion of the atmospheric eddies.