Indie Game Awards defines it like this:

"Existing outside of the traditional publisher system, a game crafted and released by developers who are not owned or financially controlled by a major AAA/AA publisher or corporation, allowing them to create in an unrestricted environment and fully swing for the fences in realizing their vision."

In other words, "indie" means a developer-driven game independent of the establishment. It doesn't necessarily imply a low budget or the lack of professional experience.

"indie" is just a marketing term now, it doesn't actually mean anything specific.