Hi Alan
LUT refers to "look up table". You can have 1D or 3D LUTs. D refers to dimension. Think of a displays white balance, gamma, and CMS controls as a 1D LUT, where you measure at 75% stimulus and make the display conform to rec 709. The problem with this is that the display also needs to apply the same corrections to all other values to make the display look correct. Some examples of displays that do not correctly apply this correction are the VT30s in mid and high output, and various Mitsubishi DLPs. A display that does not apply the correct corrections are called coupled.
A coupled display will require a 3D LUT. Think 3 dimensional, where not only the 75% stimulus values are manipulated, but also each gamma point of the RGB chroma channels, then in addition (depending on need), many other (up to 1000) points within the 3D volume of the color gamut.
Gregg