To deafen is to make someone permanently or temporarily unable to hear, especially with a very loud noise. If the music at a party deafens you, you'll probably go home early.
Things that might deafen you include a fire truck's siren, your brother blowing his trumpet in your ear, or an explosion. You can also use the word in a more figurative way, when something makes you feel overwhelmed by its loudness: "I'm sick of living on this busy road — when the bus goes by, it deafens me!" The earliest verb with this meaning was deaf, which became deafen by the late 16th century.