Lookup table is like a dictionary for color.
In digital imaging systems color is recorded using numerical values. The numerical values represent intensities or coordinates of the color space in use by the system. Often times red, green and blue (RGB) color model is used to represent color.
Let say you have an image editing program on your computer and are able to create a solid color with RGB value of 0, 100, 0. This value would create a certain green color on your screen. Let’s assume you like this color. In fact you like it so much that you go down to the hardware store and ask the associate in the paint section to mix you a can of 0, 100, 0 green.
Although the color system they use in the hardware store may have a color expressed with 0, 100, 0 value, your numbers would certainly not produce the same color you saw on your computer monitor. The numerical values are unique to the color space your system uses.
LUTs (lookup tables) are used to translate numerical values from one color space to another so color perceptual intent can be maintained across different imaging systems. In plain speak, a LUT helps your green stay green whether it’s on the screen, digital projector or in a can of paint. If color spaces are foreign languages, a LUT is a dictionary.