Bits - Originally called bit depth is the amount of color information stored in an image.
Higher the bit depth of the image means it has more color information in it. But it also increases the file size of the image.
1-bit image can store only two colors -black and white.
As you asked 8-bit images can store near about 256 possible colors.
1 bit - 21 = 2 colors
2 bit - 22 = 4 colors
Similarly 8 bit - 28 = 256 colors
16 bit- 216 = 65536 colors