Look Up Tables, or LUTs, are simple tables that match a specific input with a more desirable output. LUTs are useful in replacing common complex computations, since it takes much less time to retrieve information from memory than to perform the calculation from an equation.
LUTs are most commonly used in film for color correction. They can be applied to footage as a filter in creating certain looks. However, they are more useful in simulating the color space of different formats so that it can be color corrected for the final viewing.