During your workout you are primarily utilising both carbohydrate and fat as primary sources of energy. Fat tissue is constantly being broken down in the body and consequently, fatty acids are available in the blood stream. These fatty acids are delivered to various cells (including muscle cells) to assist in energy generation. A similar story is true with carbohydrates, where blood sugar (glucose - what results from broken down carbohydrate) is delivered to organs and tissues to maintain normal function. When exercising, your muscles also utilise glycogen, which is the muscles stored carbohydrate.
The bout of exercise that you undertake is a form of physical stress. You stress your muscles to the point at which there is a significant degree of cellular damage. Upon completion of the workout, your body goes to work straight away at repairing these cells. This is accomplished through the utilisation of fatty acids, carbohydrate and also amino acids (obtained from proteins). Essentially, your muscles are "re-building" themselves.
You can see that as this repairing (or recovery) process is being undertaken, a lot of energy is being expended by the body to recuperate. This is where a significant degree of fat tissue can be broken down.