The mitochondrial membrane electron transport chain is the instrument which allows the domestication of oxygen, and oxydations to be transformed not into heat but into "soft energy": ATP. Each mole of ATP can generate 8000 calories. Each individual manufactures & destroys every day 40 to 80 Kg of ATP ! That represents around 1 billion calories per individual per day. If you multiply this figure by 6,5 billion human beings, that corresponds to the energy generated at Hiroshima. Thanks to mitochondria, this energy is used for muscle and heart contraction, the brain, eyes, all our organs, and maintaining sodium outside of cells and potassium inside (the Na/K ATP dependent pump of our cells uses up half of all the ATP we produce).
Phosphate - phosphate - phosphate
ATP (adenosine triphosphate) is constituded by one base (adenine), a sugar (ribose) and 3 phosphates. The bond between the 2nd & 3rd phosphate is a "high energy bond". ATP is pivotal for thousands of enzymatic cascades by transfering this 3rd phosphate thanks to kinases (see Human Kinome)