I can't either. And the funny thing is, before I understood my software, I was taking only one file (either just the left or right channel) from a stereo split and burning just that file to cd. I couldn't understand why all my mixes sounded mono and things that were hard panned sounded strange.
I use the stereo split when I recieve files from other people. They send me a wav file with the click on one side and the instrument on the other. That way I can line them up with the rest of the music.
I also use it when I mix to stems. Some programs don't support stereo tracks so I send them as split tracks. That way anyone can put the files in anything and it will work.
I also had to send in my final mixes to a mastering house in Stereo Split or as he put it (dual mono)I assume it was so that he could process the 2 seperately and then recombine them
I just used stereo split when mixing down some tracks to take to a different studio. I had miced a cello with a couple of mics and I wanted to keep each track separate for future flexilibity, but I wanted to do a bit of processing and editing, so I did a mix down to stereo split with the two tracks hard panned. Now I have all the editing perfected on one wav file, but the tracks are still separate.
I have used this not for final mixdowns, but when bouncing some tracks (for example a VSTi output), so I can then process them differently and have a layered composit. This is specially useful for things such as basses, where I'll leave one untreated, and the other hi-passed, slightly distorted and mixed in lower, just to bring it into focus.