When something makes a noise, it sends vibrations, or sound waves, through the air. The human eardrum is a stretched membrane, like the skin of a drum. When the sound waves hit your eardrum, it vibrates and the brain interprets these vibrations as sound. Actually, as most things having to do with the human body, it is a little more complicated than that.
After the vibrations hit your eardrum, a chain reaction is set off. Your eardrum, which is smaller and thinner than the nail on your pinkly finger, sends the vibrations to the three smallest bones in your body. First the hammer, then the anvil, and finally, the stirrup. The stirrup passes those vibrations along a coiled tub in the inner ear called the cochlea. Inside the cochlea there are thousands of hair-like nerve endings, cilia. When the Cochlea vibrates, the cilia move. Your brain is sent these messages (translated from vibrations by the cilia) through the auditory nerve. Your brain then translates all that and tells you what you are hearing.