What is indie?

I've visited many book review sites lately, and many of them say that they don't accept self-published or indie titles. I wonder: what is an indie title? Or an indie publisher?

The definitions I see online are varied. Anyone has an idea? Does it depend on how many titles a year they produce, or whether or not they pay royalties to their authors, or if they take money upfront from the authors? The latest would be called a vanity press, I think. I'm confused.