Why do our ears ring after we listen to loud music?

Loud sounds can damage the hair cells in your cochlea of your inner ear. This causes some degree of hearing loss and your brain tries to compensate by turning up the gain control so the signals from remaining healthy hair cells are amplified. This also amplifies random noise in the signal, which we hear as a ringing. Prolonged or repeated exposure to loud noises can damage or kill the hair cells for good.