The number of bits will define how many possible colors an image can display. An 8-bit image will be able to display a little more than 16 million colors, whereas a 16-bit image will be able to display over 280 trillion colors. If you try pushing a lower bit image beyond its means it will begin to degrade shown as banding, and loss of color and detail. Nathaniel Dodson over at tutvid explains what the benefits of higher bit images in his visual breakdown.
Color depth is very important to show photographs the way you intend for your target audience. The greater the bit depth of an image the greater a number of colors that you have to play with in post-processing. As the bits increase, the number of colors increases exponentially. For example, a 1-bit image has two colors, a 2-bit image is 4 colors, and an 8-bit image has 256 colors per channel of red, green and blue.
The argument of a RAW image vs JPG can be boiled down to an argument of bit dept. The 14-bit RAW images captured by modern cameras are able to recover up to 5-stops in some cameras, capturing an image in a JPG limits your ability to recover highlights or recover shadows, and remember color profiles, exposure info, contrast, and sharpening are also baked into JPGs.
There is a caveat to higher-bit images, and that’s the fact most modern consumer displays don’t take advantage of the full gamut, only displaying about 16 million colors anyway.