Bit depth is how many steps each value can take. 8 bits gives 256 shades per colour channel; 10 bits gives 1,024. Too few steps and smooth things turn into stairs: skies into stripes, quiet sound into hiss. Below, the same sky is stored at the depth you choose, then edited the way a photo app would.
Audio stores the air pressure thousands of times a second, each sample rounded to the nearest step. A quiet note uses only a few of the steps, so its rounding error becomes audible hiss. Each extra bit lowers that hiss by about 6 dB.