A certain type of musical artist oriented toward "hipsters" and those who love them. This term was largely coined by the blog Hipster Runoff and then co-opted into the music blogosphere. These bands tend to attract a huge amount of hype, most importantly from Pitchfork leading up to their debut album, or in some cases, their second album that is supposed to represent a major advance on the first. Then, Pitchfork gives them a 9.1 or whatever and everyone flips out, and the "buzzband" becomes, at least, just another band.
Recent examples of buzzbands include Tapes 'n' Tapes, Grimes, Vampire Weekend, The xx, Cults, Fleet Foxes, and most recently, CHVRCHES.
Pitchfork is really hyping the latest buzzband's new album by positively reviewing all of their singles and posting multiple music videos.