This is a subtle modification to the standard push-up, but it's incredibly effective at improving your form and mechanics, mainly because you don't have to worry about knocking your face into the ground while using the standard hand-to-floor placement.
Although the upper torso and face should stop millimeters above the surface at the bottom of a standard push-up, you'll often see people pull the head up, look up, sink their hips, or shorten their range of motion as a means of subconsciously avoiding any harm to their face.
The ledge push-up eliminates that fear altogether, allowing you to comfortably hone in on the ideal push-up mechanics without worrying about spoiling your imagined good looks.