Some of the best indie bands are rapidly catching up with more mainstream artists as leaders within the music industry. Bands are viewed as independent once they release music minus the backing of one of the major record labels. This humbler approach allows musicians the freedom to release music which is more experimental to get a more targeted niche audience. - che-val
Without the backing of a label, the artist features a freedom to be more experimental with arrangements of songs. Often times, these artists will also be recording in small studios, as well as their own home studio, so they are not pressured by time or budget to rush through the recording and writing process. Since instant mass appeal is not the primary concern of many indie bands, you'll often find extended instrumental pieces, songs with odd lyrics (exclusively for the sake to be odd), and you can almost always bet on many friends and acquaintances from the artists contributing creatively for the recordings.
Most fans love when a common indie bands put out special releases. Albums such as live recordings, acoustic versions, and remixes are extremely popular. It also helps the artist to construct a community of loyal and hardcore followers who'll continue to pour money and support into what the band is doing. Many artists are taking even further advantage of this by allowing fans to have input on creative decisions like set lists, B-side song suggestions, etc.
Fans of indie bands love their favorite artists continue to be accessible, preferring small concert venues to large arenas. Indie music isn't featured on the radio, and listeners often discover new bands through word of mouth or demos available on their favorite label's website. For almost any concert-goer who is interested in finding something quite different, the best indie bands provide a great antidote to competed, repetitive, Top 40 music. - che-val