Atonality is a way of writing music that is not based on a key — there is no home note that the piece keeps coming back to. In most songs you know, the music belongs to a key (C major, A minor, and so on); your ear waits for that centre. Atonal music lets that centre go, so the notes do not pull toward one tidy home. The word belongs mainly to talk about Western art music from the early 1900s on, not to pop, folk, or a noisy guitar solo. People sometimes use it loosely for anything that sounds harsh or 'wrong,' but a harsh song can still have a key. Atonality is a method, not a synonym for ugly. Though actually, even atonal composers are often following strict rules; it only sounds random if you have not learned the language yet.