Why do you need to set 16 bits/channel to work with brushes?

Question

Adobe Photoshop

What does this give us and what is the advantage over 8 bits / channel?

Answer 1

It is desirable to use 16 bits in all cases where multiple image processing is required. Drawing with brushes is a special case of such processing. If I draw a semi-transparent brush over the same place 20 times, then the pixels there will somehow be averaged and blended 20 times. At 8 bits, the accumulated error can be noticeable (posterization, and so on), and at 16, it is negligible.
So it's better to keep all working originals in 16 bits, and use 8 only for the final result, which will only be looked at.

Answer 2

16-bit color is mainly used in RAW photos, which is why you can get a lot of details out of the photo (either one or the other, because the monitor works in 8-bit mode for one damn thing).
In fact, the bitness of color means the number of gradations in the channel. 8 bits = 2^8 = 256 gradations for each of the channels (R/G/B, C/M/Y/K, so by the way, the CMYK gamut on the target profile with a wide coverage contains much more colors than RGB, due to the fourth channel and an additional 256 gradations; that is why in print you can achieve shades that you will never see on an electronic device).
Accordingly, 16-bit color contains ... well, a lot of colors) But this mode is suitable only for prepress on awesomely expensive monitors, and ordinary mortals only need to edit pictures before outputting them to the usual 8-bit mode.
It's easier to see for yourself - load RAW into Photoshop and play with it (like through the Camera RAW filter, I don't know, not an expert) - watch how the details change in the photo to clearly see how many details are actually stupidly destroyed in eight-bit.