Proton motive force refers to the energy stored as a result of a proton gradient across a membrane, which is crucial for ATP synthesis in both mitochondria and chloroplasts. This electrochemical gradient is created by the active transport of protons (H+ ions) out of the mitochondrial or thylakoid lumen, resulting in a higher concentration of protons outside than inside, generating potential energy that drives ATP synthase to produce ATP during cellular respiration and photosynthesis.