The initial research was to see if alternate day calorie restriction had the same benefits as every day calorie restriction (there is evidence that restricting calories with optimum nutrition has health benefits over and above weight loss). The original idea was that it's easier to restrict alternately than every day (i.e. easier to stick to if you're very hungry one day but can eat what you like the next, than being a little bit hungry every day).
Clinical trials then showed that there were additional benefits to alternate day restriction. Firstly, there is no slowing down of metabolism which does occur on all other diets, even if just a little. Secondly, there are other health benefits which show that alternate day restriction improves health (it has an anti-inflammatory and an anti-ageing effect) over and above simple calorie restriction.
All this is taken from the book - I'm not an expert in nutrition by any stretch of the imagination!