The citric acid cycle (AKA the TCA cycle, AKA the Krebs cycle) is an incredibly important set of chemical reactions which is at the centre of how all aerobic organisms function. It is also really complicated at first glance.
Essentially, the purpose of the citric acid cycle is to extract as much useful energy as possible from macronutrients in the diet: glucose from sugars, amino acids from proteins, and fatty acids from fats. All of these molecules can be turned into a molecule called acetyl-CoA, which is the raw material for the citric acid cycle. The major function of mitochondria, the organelles which have been described as the ‘power stations’ of the cell, is to use this molecule to produce ATP (adenosine triphosphate).
Through a series of chemical reactions, the chemical bonds in acetyl-CoA are broken down and rearranged, releasing energy which is used to reduce (add hydrogen atoms to) the molecules NAD+ and FAD. This produces the energetic molecules NADH and FADH2, which are necessary for oxidative phosphorylation to occur.
In oxidative phosphorylation, the energy of these molecules is used to force hydrogen ions out through the inner membrane of the mitochondrion. When these ions are released and allowed to flow back across the membrane, they power a channel - ATP synthase, which acts like a turbine in a dam - which forms ATP from ADP (adenosine diphosphate) and a phosphate group.
All of this is important because ATP is the ‘energy currency’ of the cell. The energy made available with the splitting of phosphate groups away from ATP can now be used in a vast range of chemical reactions all across the body, from the firing of neurons in the brain to the formation of urine in the kidneys.