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Why are mitochondria often called the powerhouses of the cell?

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Fluorescent confocal image of HeLa cells with green microtubules outlining cell shapes, red mitochondria, and blue nuclei. — mitochondrion Mitochondria (red) are found throughout the cytoplasm of almost all eukaryotic cells (cell nucleus is shown in blue; cytoskeleton is shown in yellow).

Mitochondria are referred to as the "powerhouses of the cell" because they are responsible for producing the adenosine triphosphate (ATP) necessary for cellular survival and function.12

This process occurs through cellular respiration, where mitochondria break down products from the metabolism of sugars, fats, and proteins. The production of ATP involves several key stages:34

Tricarboxylic Acid (TCA) Cycle: Taking place in the mitochondrial matrix, this cycle oxidizes fuel molecules and transfers hydrogen atoms to coenzymes, forming NADH and FADH $_{2}$ .354
Electron Transport Chain: Located in the inner membrane (cristae), this chain uses the energy from electrons donated by NADH and FADH $_{2}$ to pump protons across the membrane, creating an electrochemical gradient.56
Oxidative Phosphorylation: The energy stored in this proton gradient is used by the enzyme ATP synthase to convert ADP and inorganic phosphate into ATP.56

By capturing chemical energy in the form of ATP, mitochondria provide the essential fuel required for various life-sustaining cellular activities.32