The term 'indie' or 'independent' comes from the (post) punk age when bands would release records on their own labels. As these were usually guitar-based or 'alternative' acts, 'indie' became a tag to describe the kind of music - The Smiths and New Order were arguably the biggest 'indie' bands of the 80s. Nowadays, most well-known 'indie' bands eg Kaiser Chiefs, are on major labels and, ironically, what would once have been termed 'alternative or 'indie' are now mainstream eg Oasis, Stereophonics, although these could also be termed 'indie rock', being somewhat 'harder' than some indie bands.
It's a bit of a loose category and, in my day (80s) had a lot of snobbishness attached to it. Bands were only 'cool' when on small independent labels and were usually dismissed as having 'sold out' if they signed to a major label. There was a huge furore when The Smiths signed to a major. I may be too old to have an objective view but such 'snobbery' doesn't seem as prevalant these days.
Hope that helps!