What is it that defines "indie" music?

Good question. It was easy back in the 90's when it relied on what record label.... indie : independent label. Now though it refers to a type of rock music. Basically soft, intelligent, non-commercial rock music with integrity, mostly coming from the British Isles but not exclusively. Best I can do.

For me I would rather call it college rock because, it always holds true to that formula, really thin guitar driven music with a poppy and folksy edge.

Pretty much what The Joker said. It was easier in the past as it meant a style played by bands on small (indie)pendent labels, but nowadays many bands that fall into that category are on massive major labels. It is often rock music but slightly less aggressive and bludgeoning than other styles, and often more introverted.

An independence from major corporations.

It's not part of popular music and more than likely the singer or band is not signed to a major record company or if they are signed it will be to a small and relatively unknown record company.

So long as it isn't mainstream sounding.