A LUT, or "look-up table", is a color grade preset you can apply to your footage to visually enhance it. Similar to a filter, they are used to reach your desired overall look.
All the relative information about using LUT's in your workflow can be found in the manual here (section 6.8.14. LUT).
LUTs also provides a powerful way to provide a one-click grade, simulating specific film stocks and processing techniques. Applying a LUT to flat footage can produce high-quality results very quickly.
The LUT effect, available in Creator and Pro plans, can import .cube LUT files. HitFilm itself doesn't provide any LUT's but these can be found on many sites.
To use a LUT:
1. Add the LUT effect to your layer, from the Effects panel.
2. In the controls for the LUT effect, click the Folder icon to the right of the LUT File property.
3. In the File browser that opens, navigate to the .cube file that you wish to use, and select it. The LUT will be applied to your layer, and the path to its location will be shown in the effect controls.