Here's why:

* Proton Motive Force: The movement of protons (H+) across the inner mitochondrial membrane (in cellular respiration) or across the thylakoid membrane (in photosynthesis) creates a proton gradient. This gradient represents stored potential energy known as the proton motive force.

* ATP Synthase: ATP synthase is a protein complex embedded in the membrane. It has two main parts:

* F0 unit: This part spans the membrane and acts as a channel for protons.

* F1 unit: This part protrudes into the matrix/stroma and is responsible for synthesizing ATP.

* Mechanism: As protons flow down their concentration gradient through the F0 unit of ATP synthase, the energy released from this movement drives the rotation of a central shaft within the F1 unit. This rotation causes conformational changes in the F1 unit, leading to the phosphorylation of ADP to ATP.

In essence, the proton gradient provides the energy necessary for ATP synthase to produce ATP.