Something that is sweet, almost to the point of being sickeningly so. As a derogatory descriptive, it means something that is affectedly dainty or quaint, or is way too sentimental.
In American English it often refers to a type of simple sweet pop music, but in British English it is used much more widely for things that are nauseatingly cute or precious. It comes from the way the word sweet sounds when said in baby talk.
Belle and Sebastian are the Beatles of twee.