LUT stands for ‘lookup table’. Essentially, it takes the colours in an image and remaps them on to new ones. It really is a table consisting of a large grid of colour swatches and how they should be adjusted in the converted images. Its closest equivalent is the device profiles used in colour management systems, which work on a similar principle, but LUTs are usually designed for creative effects rather than colour correction.
LUTs are often used to simulate classic films or filter effects. They’re commonly distributed as preset effects for programs like Lightroom, Capture One and now Skylum’s Luminar image-editor. It is possible to create your own LUTs, but it’s a somewhat technical process.
The advantage of LUTs for image editors is that they are, in theory, software independent. The same LUT (or image effect) can be used in any software that can import and apply lookup tables.
The disadvantage is that the LUT effect can’t be edited. It’s a straightforward colour conversion with no user-editable settings, though you can of course add other image adjustments in the software used to apply the LUT.