An indie role-playing game is most commonly defined as any RPG where the game is owned and controlled by its creator.
At the very least, this is the definition used at The Forge, and certainly applies to most games that get tagged with the label, such as Inspectres, Sorcerer, the Wuthering Heights RPG and Universalis.
Most indie RPGs push the boundaries of role-playing past the very Simulationist or dysfunctional Gamist methods of the more well-known games like Dungeons and Dragons and White Wolf's Vampire: The Masquerade.
Certainly it's true that a game of OctaNe is a lot more fun than a dungeon crawl, Xcrawl nonwithstanding.