Indie rock takes its name from "independent," which describes both the do-it-yourself attitudes of its bands and the small, lower-budget nature of the labels that release the music. The biggest indie labels might strike distribution deals with major corporate labels, but their decision-making processes remain autonomous. As such, indie rock is free to explore sounds, emotions, and lyrical subjects that don't appeal to large, mainstream audiences -- profit isn't as much of a concern as personal taste (though the labels do, after all, want to stay in business).
It's very much rooted in the sound and sensibility of American underground and alternative rock of the '80s, albeit with a few differences that account for the changes in underground rock since then. In the sense that the term is most widely used, indie rock truly separated itself from alternative rock around the time that Nirvana hit the mainstream. Mainstream tastes gradually reshaped alternative into a new form of serious-minded hard rock, in the process making it more predictable and testosterone-driven.
Indie rock was a reaction against that phenomenon; not all strains of alternative rock crossed over in Nirvana's wake, and not all of them wanted to, either. Yet while indie rock definitely shares the punk community's concerns about commercialism, it isn't as particular about whether bands remain independent or "sell out"; the general assumption is that it's virtually impossible to make indie rock's varying musical approaches compatible with mainstream tastes in the first place.
If music be the food of love, play on, Give me excess of it; that surfeiting, The appetite may sicken, and so die. ― William Shakespeare
There are almost as many reasons for that incompatibility as there are indie-rock bands, but following are some of the most common: the music may be too whimsical and innocent; too weird; too sensitive and melancholy; too soft and delicate; too dreamy and hypnotic; too personal and intimately revealing in its lyrics; too low-fidelity and low-budget in its production; too angular in its melodies and riffs; too raw, skronky and abrasive; wrapped in too many sheets of Sonic Youth/Dinosaur Jr./Pixies/Jesus & Mary Chain-style guitar noise. (Source: allmusic.com)