I'll do my best here...
If you look at any (to my knowledge anyway) production bike so far, the brake calipers are held to the forks by fasteners that extend parallel to the front axle. Radial brakes, which are found on most high end race bikes these days hold the caliper on differently. As you may have guessed, the fasteners extend radially (sort of) inwardly toward the front axle. That is, they are parallel to the plane of the front wheel. You'll see it if you look really closely at the pictures.
The reasoning behind all this is that fasteners are much better in tension/compression (as they are in the radial setup) than they are in shear (as they are in the conventional setup). The radial setup provides a stiffer brake caliper mounting, resulting in better brake feel.
Hope that covers everything, but I'm sure someone will find something else to add.