Adipose tissue contains adipocytes that store triglycerides in intracellular vesicles. In resposnse to homoestatic pressures the tirglycerides are converted to glycerol and fatty acids. The fatty acids can then leave the cell, enter the blood and be transported to other tissues which need the fatty acids to synthesize ATP.
Fatty acids from the blood enter the cytosol of cells by facillitated diffusion and then enter the matirx of mitochondria. In the mitochondria the fatty acids are broken down in a process called beta oxidation to acetylCoA, NADH and FADH2. The acetyl CoA then enters the Krebs cycle which results in the further production of NADH and FADH2.
The two figures below offer a rough comparison of the yield of NADH and FADH2 from a six carbon carbohydrate and a six carbon fatty acid. You should notice that the six carbon fatty acid yields much more NADH and FADH2 than does a six carbon carbohydrate. Thus when completely metabolized to CO2, on a pound for pound basis triglycerides yield more ATP than does glycogen.