Here's how it works:

1. Electron Transport Chain: Electrons from the breakdown of glucose (glycolysis and the Krebs cycle) are passed along a series of protein complexes embedded in the inner mitochondrial membrane. This process releases energy.

2. Proton Pumping: The energy released from electron transport is used to pump protons (H+) across the inner mitochondrial membrane, creating a proton gradient.

3. ATP Synthase: The proton gradient drives the movement of protons back across the membrane through a protein complex called ATP synthase. This movement of protons powers the enzyme to synthesize ATP from ADP and inorganic phosphate (Pi).

Oxygen is crucial for oxidative phosphorylation because:

* It is the final electron acceptor in the electron transport chain. Oxygen combines with electrons and protons to form water, thus regenerating the electron carriers for further electron transport.

* Without oxygen, the electron transport chain would stop, and the proton gradient would dissipate. This would prevent ATP synthesis.

In short, oxidative phosphorylation is the primary way that cells produce ATP in the presence of oxygen. It is a very efficient process, generating significantly more ATP than other pathways like glycolysis.