I would personally say that "alternative" as a genre has, to me, always simply meant something other than what is taking place in the music mainstream. That is not to say it is the same as "indie" (or music that is released on an independent label--although the definition of that term is beginning to change too) but as one would expect, there's often a fair amount of overlap between indie and alternative.
Three examples to illustrate my classification system:
-I would considerNirvana's "Nevermind" a alternative album (at the time of its release, it had almost nothing in common with what was happening in the mainstream), but having been released and promoted via a major label, it is by definition not an indie album.
-Interpol's "Turn on the Bright Lights" album would be considered both an alternative AND indie album' as it sonically had little to do with mainstream trends at the time of its release, and it was published by famed independent label Matador Records.
-And finally, Robyn's self-titled album from 2005--at least, the original version--would be considered an indie album, but not an alternative album, because although it was self-published on the singer's own independent label, the music was in keeping with mainstream production and aesthetic values.
This is completely subjective, but I hope my explanation as to how I define and think of "alternative" music helps you arrive at your own opinion and ideas about the genre.