what exactly do you want to know?
8-bit means 2 to the power of 8. = 256 different brightness levels for each colour channel. extreme or repeated editing of an 8-bit image may lead to posterisation.
16-bit doesn't exactly mean 2 to the power of 16. photoshop has "only" 32000+ levels, instead of 65000+ as might be expected. but 35mm based dslrs mostly create 12-bit raw files (4096 levels); other backs may have 14-bit (16000+ levels). basically, you get more levels to play around with during raw conversion and in 16-bit editing, so that when you convert "down" to 8-bit, the transitions are smoother.