I'm sure the scholars on this site will give you a waay better response later, but for now..
A LUT is short for a Look Up Table. In regards to creating images, a Look up Table is used (mostly) to create a linear image from a logarythmic source, ie a TIFF file (linear) from a RAW source (camera RAW).
You would use a LUT to interpret a RAW camera image into a linear form, making an exposure in the process.
I use LUT's in my Andromeda workflow, an upgrade to the DVX100 video camera which allows it to record RAW ccd data. When rendering out the RAW data into a quicktime or a series of stills for editing, I apply a LUT and it grades the image, ie renders it out in a certain coloring and with certain grayscale parameters. Kind of like making a print in photography, I guess.
This is not a simple explanantion and I'm sorry, but if you search for LUT's on this site:: www.reel-stream.com, in the forum, the moderator Juan P. has written many many great and simple explanations of LUTs and why and where you use them as well as the process and theaory behind them.