Dr McBride used this diet on her autistic child and found that it cured him not only of his stomach ailments, but also his autism. She has since recommended this diet to anyone who has issues with any sort of stomach, intestinal, and neurological disorders.
This diet is a very restrictive diet that some people may need to be on for years.
You can order Dr McBride's book which is exhaustive if you want all the science background to this diet. Or, if you only want the protocol in simple steps you can get GAPS Guide by Baden Lashkov.
The basic premise of this diet is to heal the gut through easily digested healing soups made with bone broth while growing and regulating your good intestinal bacteria. Slowly, you will add foods back into your diet as long as your body can handle them. This sounds tough, but if you're dealing with severe symptoms this diet will quickly get control of them and eventually take them away permanently!
Since others have a lot of good research out there, I'm going to include their links:
GAPS introduction stage
GAPS experience review