The ATP-ADP cycle in aerobic cellular respiration involves the conversion of adenosine triphosphate (ATP) to adenosine diphosphate (ADP) and inorganic phosphate (Pi) during energy-releasing processes in the cell. When ATP is hydrolyzed, it releases energy that powers various cellular activities. This ADP can then be re-phosphorylated back to ATP through processes like oxidative phosphorylation in the mitochondria, where energy from electrons is used to add a phosphate group to ADP, completing the cycle. This continuous regeneration of ATP is crucial for sustaining cellular functions.