Bit depth is used to control how many colors an image holds. The more colors, the smoother the image.
1-bit is two colors (black and white), 2-bit is four colors, 4-bit is sixteen, 8-bit is 256 colors, 16-bit is 65536 colors, etc.
The number of colors at any bit depth is 2 to the power of the bitdepth. For instance, 8-bit = 2 to the 8th power = 2x2x2x2x2x2x2x2 = 256 colors.
If game uses alpha or heightmaps, then they are additional channels that can be added to the bitdepth number.
16-bit is 65536 colors without any additional channels, but if you want to add an alpha channel, then 16 would be divided into RGB and alpha, which can be done a number of ways. For example, if you use 4 bits each for Red, Green, and Blue, then that is (4 + 4 + 4) which leaves 4 bits for the alpha, which is 16 grays. Or you can use 5 bits for each RGB which means you get 1-bit for alpha, which is only 2 grays, but this gives you more RGB colors to work with. It's a trade-off.