A look-up table does what its name says: for a given input color, it looks up what that color should become. A 1D LUT adjusts each channel independently and handles contrast and gamma. A 3D LUT maps the full color cube, so it can shift hues selectively — the type used for actual looks.
The two main jobs are worth separating. Technical or conversion LUTs transform log footage into standard color space so it looks correct — a necessary, largely invisible step. Creative LUTs apply a stylised look on top. Applying a creative LUT before the conversion, or stacking two conversions, is a common route to footage that looks broken.
LUTs are a starting point, not a finish. They apply the same transform regardless of exposure or white balance, so footage that was not exposed as the LUT expects will band, clip, or shift oddly. Standard practice is to balance the shot first, apply the LUT, then grade on top — and to treat any LUT that instantly looks perfect with suspicion.