It's common knowledge that muscles primarily use carbohydrates as "fuel" for movement. The rise of the ketogenic diet amongst the athletic community has also shed light on the fact that fat is also an energy source that can be used for muscle movement.
What you may not know is that the body's use of these fuels is completely dependent on exercise intensity.
Below is a simplified diagram (ref. The Science Of Sport) showing a simplified version of the relationship between the two fuels.
So, if you're an athlete that prefers short bursts of high intensity training, such as in CrossFit, sprinting and many field sports, then you'll tend to live in the higher carb usage camp. When training at this intensity you'll burn through your glycogen stores quickly and need to replenish what you have used for subsequent training session performance.
But I want to burn fat so that I look better!?!
Firstly performance should come before looking good (of course), but we acknowledge that aesthetics can be a nice side effect of being athletic.
Secondly, the model shown above is simplified for textbook type teaching. What isn't shown is what happens after training. When you switch to recovery mode your body will focus on using the carbs you consume (or the protein if carbs aren't available) to replenish that which is lost. This means less of what you eat post training will be turned into fat.
In addition, the body will continue to use up fat stores for your usual baseline energy needs - especially as you're now low on the preferred carbohydrates.
Bottom line: Carbs are a vital energy source if you're going to train at a higher intensity... and don't worry, your waistline will still love you for it.