More Colors, less banding and toothing, and more accurate colors.
Here's how it works
A bit is a single piece of digital data coded either a 0 or 1
A byte is made up of 8 bits or a string of 8 0's and/or 1's run together to create a single number with 8 places.
To get the number of unique combinations of 0's and 1's based on the number of places you string together, use exponents with a base of 2 (representing 0 or 1) and the appropriate exponent representing the number of places you are going to string together. Thus for an 8bit number each unique combination of 8 0s or 1s represents one unique color. The an 8bit depth image can display up to 256 different colors. The matrix below expands on this idea.
8bit = 2 to the power of 8 (01010100)
16bit = 2 to the power of 16 (0001010001001000)
24bit = 2 to the power of 24 (010010001000100001001000)
32bit = 2 to the power of 32 (00001000000010010000100000000001)
Thus for colors these "bit depths" give increasing variations:
8bit = 256 colors
16bit = 64,536 colors
24bit = 16,772,216 colors (True color or the limit of human vision)
32bit = 4.29 billion colors (Beyond human vision or our ability to distinguish different colors)
It is not just banding you would want to avoid through using high bit depths but also you will see more accurate color. With 256 bit images a nice skin tone might be converted to orange. With 32bit it is more likely that a given skin tone (or whatever) will be displayed correctly - at least one of those 4.29 billion colors will be close

Thus for color accuracy (assuming everything else is calibrated properly) go for the higher bit depths.
Cheers,
Brent
In personal computers, whats the difference between 16bit and 32
bit settings in the display? Where would I most likely actually
see the difference?
Thanks,
Jarrell
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D100, 5700 and 990
I child proofed my house, but they keep getting in!
FCAS Member, dslr division
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Brent Haydamack
9-9-5, S-u-n-p-a-k P-Z--4-0-0-0-A-F