Indie means one thing only: it was developed by an independent studio. The problem is, everybody that has ever coded a basic "hello world" thinks they should be able to make a game. Indie has come to be interpreted as very low budget exactly because the vast, vast majority of indie titles are made by a single person or a small group on little to no budget in a short time period, usually with quality reflecting that fact.
Generally speaking, most quality indie titles fall in the realm of A, like Bastion or Transistor. The thing is, so many indies aren't even A quality that they've basically earned their own classification on every level.
As for AAA, AA, and A, for the most part, they're relatively BS labels that we use so that we can insist on the fact that particular games were a waste of money, and that other games are so good despite their lower budgets. It's something mostly used for list wars, and is completely and utterly useless otherwise, especially since the labeling is always a vague, subjective combination of IP popularity and assumed budget.
