In imaging, think of Web Safe colors, that is actually a very simple form of a LUT, or you could also think of curves.
They actually remap the color values, based on the color lookup CLUT. These are essential tools in color grading and emulating classic film looks.
A very common use for LUTs is previewing, or converting footage shot in a log mode. These were originally used by filmmakers and videographers and applied to video to create film looks in movies and to convert from one color space to another. Transform your Photos with LUTs in Photoshop, THE USER GUIDE.