Proofing is an interesting process, and for some reason it is called 'proofing', not 'proving'. I suppose it is a process of fermentation, but the production of alcohol isn't the aim.
Proofing is all about ripeness. A good loaf of bread comes from three or more good proofs, each one being ripened for long enough for the gas bubbles to fully expand inside the gluten bubbles which make up the dough. This expansion is paused by 'degassing'. This process is often referred to as 'punching down', though I have no idea why anyone would want to punch dough. Some weird testoserone fantasy, like dough was some uncontrollable beast that grows and grows, and must be defeated.