calorie cycling is a way to keep your metabolism jolted so to speak. Our bodies try very hard to keep us in 'HOMEOSTASIS'. That is why if we start losing a bunch of weight--the body senses starvation. Let's say you have dropped your caloric intake from 1800 to 1400. You try to maintain that number every day. The body becomes more efficient at only using 1400 cs a day and then it adjusts your metabolism so you can eat less and still not lose weight. The body constantly adapts. So the theory of cycling calories is to KEEP YOUR BODY FROM adapting to a certain calorie limit.
For example using the website:
http://www.freedieting.com/tools/calorie_calculator.htm
my BMR is 1515. to maintain my weight I need to eat 2083 cs day.l
To lose 2-3 lbs a week I need to eat 1416 cs day.
I COULD do that only eat 1416 cs per day. Eventually my body will adapt (plateau my weight loss). However, I could also calorie cycle:
1416 *7 = 9912
but so does 1416+1416+1700+1416+1416+1558+1416 =9912
The method chic is using is actually recommended by the author of Lean Gains. He mentions on rest days that he eats fewer calories and less carbs. On heavy cardio days he eats more calories and more carbs. ON heavy strength days he eats more protein and more calories.
edited to say: when I was easing myself into a weight loss plan a couple of years ago I was just logging my intake and my weight loss amount on an excel worksheet. I noticed when I naturally zig zagged (cycled) my calories the weight loss would jump start. So I learned it was a useful tool.