For example, what IS classical music? Some guy asked me, and I didn't have a definitive answer.
It's not really time period, so how would you define it?
I'll take two- very different- stabs at answering this:
1) Classical music is music produced in the tradition of Western Art Music, consisting predominantly- but not entirely- of music produced on instruments contained in a modern symphony orchestra and other western instruments that traditionally accompany such instruments. Such music can often include instruments and musical traditions from non-western or "folk" sources, so long as the music in question aspires to be a part of, a continuation or, or an extension of the Western Art Music tradition. Moreover, non-western composers frequently write "classical"music as well, but the intent of such work is usually the folding of non-western traditions into a Western Art Music context.
Classical music is almost entirely "score based" and it is typically, though not always, "through composed" (exceptions include: the basso-continuo in Baroque music, the Cadenzas of Classical and Romantic concerti, and the aleatoric instructions in some 20th century experimental works.) In performance, while individual musicians strive to reveal the meaning inherent in the score- in a manner similar to a textual "exegesis"- strong emphasis is placed on the intent of the original composer rather than the creative extension of a work by a performer. In other words, the performer of Classical music is generally considered to be a vehicle for the expression of interpretation (whether "faithful" or, conversely, "idiosyncratic") of a "platonic ideal" of a score rather than the performer's unique qualities being the main emphasis. Once the performer becomes the predominant emphasis, the music is generally considered to be an exemplar of another "popular" stream of music. Exceptions exist, but these are typically well grounded stylistically within the traditions of Western Art Music.
The style of "Classical" is, more than anything, understood by its continuous evolution from the religious music of Medieval Europe, through various streams of styles through periods now referred to as Renaissance, Baroque, Classical, Romantic, and Modern music. A work of "classical" music is understood to be such when it appears to be an exemplar, continuation or extension of this tradition, and the intent seems to be not merely to "make reference" to such previous work, but to contribute a new voice to an ongoing exploration of the possibilities of "score based" work.
Many other tradition streams dubbed "classical" (Indian classical, Chinese classical etc,.) exist, and some intermixing occurs- but, in the Western word "classical" by itself typically means that tradition which includes those musical streams which grew out of the European sources mentioned above, and most of these other tradition streams are not understood to be a continuation of the Eurpoean Art Music tradition barring any intermixing of styles.
2) Defining genres is a futile effort. Dividing "classical" from "popular" music involves arbitrary and, often, biased distinctions and stifles creative exploration.