Cellular respiration is the process of oxidizing food molecules, like glucose, to carbon dioxide and water.
C6H12O6 + 6O2 + 6H2O → 12H2O + 6 CO2
The energy released is trapped in the form of ATP for use by all the energy-consuming activities of the cell.
The process occurs in two phases:
glycolysis, the breakdown of glucose to pyruvic acid
the complete oxidation of pyruvic acid to carbon dioxide and water
In eukaryotes, glycolysis occurs in the cytosol. (Link to a discussion of glycolysis). The remaining processes take place in mitochondria.