Type of indie pop that is known for simple, sweet melodies and lyrics, often combined with jangling guitars; twee is also British slang for something almost sickenly sweet
All Girl Summer Fun Band, Camera Obscura, Belle & Sebastian are all great twee pop bands.
Coyly precious indie pop, generally driven by jangly guitars and adenoidal or high-pitched vocals. The name "twee" was first applied to indie pop groups in England in the 1980s, like Heavenly, and was not obviously a compliment. At best, it was an affectionate insult. In the U.K., calling something "twee" suggests that it is affectedly dainty. To the extent there is currently a twee pop revival, that revival is mostly taking place in the U.S. and Scandinavia, where no one knows that they should care about the pejorative implications of the word.
The band members of Camera Obscura might not like to have their music referred to as twee pop, but they are twee as f**k.