Mach bands are named in honor of Ernst Mach the Austrian physicist and philosopher who is also the namesake for the "Mach number" (also known as Mach speed). The Mach band optical illusion is the basis for how most image sharpening, such as the "UnSharp Mask" filter in Adobe Photoshop, is effected in photo editing software.
The principle idea is that we do not see detail because of our eye's resolving power but because of tonal contrast. For example, this is an image of a wall beside an electrical socket. The lighting used was very low contrast:
Here is the same section of wall but this time using low angle lighting:
Obviously the texture of the wall hasn't changed, instead what has changed is the tonal contrast of the area and that allows us to see the texture detail.
Mach discovered how our eye/brain leverages contrast to compensate for its lack of actual detail resolving ability.
Look closely at the below image which has nine patches of grey set between a black patch and a white.
Do the grey patches appear scalloped? Lighter on the left than on the right? In fact, the grey patches are of a uniform tone as can be seen by simply moving one patch out of its context.
The scallop effect is an optical illusion. To make up for our eye/brain's detail resolving deficiency it processes incoming light in such a way as to exaggerate the contrast wherever two different tones meet. Increasing the contrast at those edges gives us the perception of more detail.
Here's how the sharpening filter in Adobe Photoshop leverages this optical illusion to make images look more detailed. First I'll apply it to the original grey patches. The top half is the original and the bottom half with the sharpening filter applied:
What PShop does is to increase the contrast at the border between different tones by creating synthetic Mach bands.
Now we'll see the same sharpening method applied to a real image.
On the left is an original globe image straight out of the camera. On the right is the globe after sharpening is applied showing the effect of creating Mach bands with image sharpening.
Here is a close-up section of the globe images to more clearly show the difference:
Technically, the sharpened image actually has less real detail because image pixels had to be converted to black and white lines bordering the actual image detail. However, despite having less detail our eye/brain perceives a sharper, more detailed, image all thanks to software leveraging the power of an optical illusion.