The cochlea is the sense organ that translates sound into nerve impulses to be sent to the brain. Each person has two cochlea, one for each ear. The cochlea is a fluid-filled, snail shaped cavern in the mastoid bone of your skull behind each ear. Tiny bones in the middle ear transmit sound from the eardrum across the middle ear and vibrate against the cochlea. Vibrations in the fluid cause tiny hair cells in the fluid inside the cochlea to vibrate and generate nerve impulses that then travel to the brain.
Many people think the cochlea is just an input device, but in fact, it is much more complex than that. It works with the brain (receiving information about what the brain would like it to do) to filter sound, before it even gets to the brain. For example, it's the cochleas which the brain tells to ignore certain sounds which the brain has determined to be "background noise".
That's why people with good hearing can hear and understand speech, even in very noisy rooms. It's also why background noise is such a problem when hearing loss damages not only your hearing, but also your cochleas' ability to filter out backgroung noise.
A hearing aid can make things louder, but it can't perform that vital cochlear function of background noise filtering. Some hearing aids do have directional microphones, which performs some background noise reduction, but it can't be as effective as your cochleas, since the hearing aids can't get the noise reducing instructions from the brain.