[schrectacular]

I think a good rule of thumb for any society's "classical" music is "what do the cultural elites coalesce around" - so in western society the political, business, and academic elites go and be elite-y at the symphony or the opera.

In India "educated" or "learned" people will be intimately familiar with many of "raags/ragas" which can be thought of as "tunes" (but they are deeper than that). These ragas are usually meant to be played at different times of day/year or to evoke certain moods. Players will improvise these raags, interpreting not only their "version" of the song, but custom jamming a version specifically for that place and time and audience. Some of these raags have a very long history. I think when people talk about "classical" Indian music this is what they mean. Temporary it's deeply historical music that is constantly evolving.

I'm generalizing and glossing over so much to be brief, and much of this varies by region and tradition, but that's a gist.

[danans]

In addition to what you've said about the eliteness, it's also music around which a rigorous theoretical system has developed.

This is on contrast to folk music, which focuses less on theory.

In India, which just as in the west, development of the theory was aided by the patronage of the wealthy/elite.

Also as in the west the theoretical system serves the purposes of preservation, reproducibility, and most of all, pedagogy.

[vatkhrt]

Its interesting that in the "long history" of some of these raags, many have moved from folk into the classical realm. To name a few - Mand, Khamaj, Desh. There is also the diffusion of some classical ragas into wider collective conscience through film music, and other forms of "light" music.