Why would a 4d texture be used for color conversion? You can perform color conversion as a post process step to convert a rendered frame's colors to a different set of colors.

You might make darker colors more blue for instance, to give it a night time feel, or just modify colors to give it a different mood.

One way of doing this is using a volume texture.  You use the RGB value of a source pixel as texture coordinates into a volume texture, where you read out the RGB value that you should replace that pixel with.

This page on the 4d texture GL extension says this though:


  Four-dimensional textures are used primarily as color lookup tables
  for color conversion.


Can anyone explain why you would use a 4d texture lookup for color grading?

Alpha (transparency) lookup doesn't seem like a plausible explanation, but perhaps something like normalizing an HDR color and using the intensity as the fourth component could be?  Or perhaps time, to be able to interpolate between two different color gradings, when moving from inside to outside and exposure is changing or something?
I think your quote refers to conversion between color spaces, rather than color grading. 4d textures could be used as lookup tables to convert color spaces like CMYK to some other space. Since CMYK has 4 components, a 3d texture wouldn't be enough.