Well, 'Indie' isn't a style of music at all. It's actually short for Independent, referring to the smaller independent record labels rather than the big corporations such as WEA, EMI, Virgin, etc.
During the 80's, Erasure were one of the most popular bands on the Indie Chart, because they sold well, and they were signed to Mute - one of the smaller labels.
Nowadays, most of the smaller 'Indie' labels have been bought out by the larger companies, so there isn't actually much Indie music left.
It always makes me laugh when I see a band who are signed to one of the big labels branded as an 'Indie' band, because they're not.