Digital Capture Basics
The camera measures three color bands, that may be more or less similar to the three bands used in the human eye. Different cameras use different base colors, that respond to colors in reality in different ways. To make the camera measurement correspond to human vision, a transform has to be made. The most basic type of transform is the "matrix" transform, which works just like the "color mixer" in Photoshop. In addition to this, most camera color profiles contain a more fine-grained correction tool, the "LUT" or "LookUp Table" correction.
In the matrix transform a certain "mix" of values in the input (the raw file) gives a certain mix in the output (the converted file). Red in the output file may be made from something like this:
Rprocessed = 1.25R raw - 0.31G raw + 0.05B raw
All of the color channels in all of the pixels of the raw file has to be transformed like this before the next correction step takes over.
The LUT, or "Look Up Table" type of correction is meant to correct for non-linear variations in the camera filters. Just as the filters may not correspond to a human eye in average color response, it may also have other non-linearities. A good color filter is like a soft sine curve - it has a well defined center peak of transmission in the color it is supposed to convey, and soft fall-off towards the colors which it is supposed to block.
But in reality, we cannot make that kind of color filter on a camera sensor. We have manufacturing limitations, and also a limited numbers of materials to mix and choose from. The filters in a real camera may have a very ragged response; it may block more on one side of the spectrum than the other and so on. It may also have very local faults. Two colors very close in hue might get separated more than they should, or made almost identical.
To correct this you need a correction "map" that can correct for very small local deviations without disturbing hues nearby. This part works like a finely resolved grid that you place over the map of possible colors. Each point on the grid has a correction value assigned to it, a modification that is applied to the data. This gives the type of correction its' name, the lookup table. It looks at the color values, "looks up" the corresponding map position and applies the correction it finds at that position.