An umbrella term used to describe a style of music that emerged in the late 80's and early 90's.
Alternative music is usually characterized by bands who have a "do-it-yourself" or non-conformist attitude; hence "alternative".
Today, the term is often thrown around by people who don't really understand what it means and think that it can be applied to any band of their choosing.
This is not true -- for a band to be truly Alternative, they have to follow the Alternative mindset; that is, they must either perform in a style of Alternative Rock already established (see Grunge or Britpop) or be avant-garde and completely throw what it considered usual or average out the window.