CLUT is short for Color LookUp Table. It refers to a technique used in older hardware to display bitmaped images. Instead of storing the color in the pixel's memory location, a CLUT based system stores an index that refers to a table of component color values.CLUTs are also refered to as palettes. The diagram below serves to illustrate how a CLUT works. In the pixel's memory address, a value of 5 is stored. This value is used to look up the 5th entry in the color table which ends up being purple.
  The value of a pixel
            |
            |                      Index   Red   Green   Blue  
            |                    |   0   | 20  |  40   |  10  |
            V                    |   1   | 10  |  40   |  30  |
  | 3 | 2 | 5 | 0 |              |   2   | 35  |  12   |  11  |
  | 1 | 1 | | | 1 |              |   3   | 35  |  12   |  11  |
  | 2 | 3 | | | 2 |              |   4   | 35  |  12   |  11  |
  | 2 | 2 | =====The lookup=====>|   5   | 75  |  40   |  75  | =====>The Pixels Color  (purple)
Simple 4x4 pixel bitmap               The color lookup table
The main reason that this technique is used is to save memory at the cost of reducing the colors available. Let's say you have a screen resolution of 640x480 and you're using 24 bit color. 24 bits is 3 bytes per pixel and that gives you 640x480x3 or 921,600 bytes needed to store the image. If you were using a CLUT system, that same image could use 640x480x1 or 307,200 bytes, which is 1/3rd the size. Of course, the first image could contain over 16 million different colors (if it had enough pixels - and it doesn't), while the CLUT image could only contain 256 different colors.

There are a few more cool things that you can do with a clut system. You can change the CLUT while the image is displayed to create an illusion of movement. This technique is often refered to as color cycling or palette animation, and it involves stuffing the CLUT with a bunch of different palettes, in a sequence. Video games often use this technique to create the illusion of flowing water, glowing hot lava, or flashing lights.

If you're doing real-time 3D graphics you can create a scene with texture maps using one CLUT representing a certain time of day, for example, morning. You could then create another CLUT that would work for the same texture maps but would represent another time of day, mid-day for example. If you smoothly fade from one CLUT to the other, you can create the illusion of changing time of day in your 3D game.