OAEs are routinely used to test for normal hearing in newborn babies.
Hearing relies on a chain of events all working together. Sound reaches the eardrum and transmits vibration in the inner ear. The inner ear spreads out the different rates of vibration which compose the sound - over the string of cells which have the job of translating the vibrations into nerve impulses. Thousands of nerves carry the 'digested' sound signal to the lower levels of the brain where its features are recognised as sound elements.
If the sound elements are correctly recognised then we eventually understand the meaning behind the sounds.
A physical problem arises when the inner ear tries to perform its sound analysis. The vibrations fade away too fast due to friction between the moving surfaces and fluids.
This would lead to dull and insensitive hearing - if it were not for another group of hair cells which have the job of supporting the vibrations and replacing energy lost by friction.
In effect, these cells replace lost sound energy by creating their own. Some of this biological sound energy leaks back out of the ear and we can detect it with computer based sound analysers.
When active otoacoustic emissions are found it proves that the cellular vibration boosting mechanism is there and working. It doesn't prove you can hear or understand sound but it's a good start. With newborns, it's a great help to know the inner ear looks (or sounds) normal. With hearing loss patients it helps to locate the cause.