^^really it's more of an aesthetic and/or marketing label than anything else. It pretty much means rock bands that, often but not always, are on indie labels, that you don't here on the radio, which experiment and deviate from "mainstream" sounds, and which don't fall under other genres such as punk, metal, hardcore, ska, etc. Even then that's a loose and incomplete definition. I could go on and on on this topic but fav indie bands of all time have got to be:
Pavement, Radiohead, Arcade Fire, Flaming Lips, Neutral Milk Hotel, Yo La Tengo, Modest Mouse, The Strokes (I know their last LP sucked), Spoon, The Smiths, and Sonic Youth.
I think cause of the time period they came out in, indie rock wasn't much of a term, but I'll throw in The Replacements and Talking Heads as those are the two bands of the post punk/early alt era that have had some of the most influence on indie rock.
Recently been listening to the new Animal collective still, Grizzly bear (it leaked like a month or two ago but it sat in my itunes w/o a listen until 2 days ago), Pains of being pure at heart, and Lotus Plaza (a deerhunter side project). Put on Person Pitch again a week ago and have been listening to that nonstop once again as well.