Ouch. Dithering is hard to explain.
I'm not entirely clear myself, but this is the best I can do (correct me, pixel masters, if I am wrong):
Dithering is a technique created for old consoles to blend colors as there were restrictions, in order to let the eye blend thinks and make them smoother and/or different colors, or for certain effects. It was later adapted for adding texture, NOT making it smoother! Right now, it's used to either add a bumpy texture, or to smooth a line out, or even to add noise for the sake of adding noise. Dithering, even though it only originated as a checkerboard pattern is now a very loose term; you can dither tons of different ways. Basically, dithering is an interesting way to bridge two colors, and checkerboard is the most dull yet most common.
Something like that?
Really, pixel-peoples, correct me because I'm almost SURE I'm wrong somewhere.
Thanks.
Shrike