Wikipedia has an article on the Western Canon that has a good summary of the idea:
But I come more and more to think that it is a poor word to use with regard to music, however accurate it may be in literature. This is prompted by getting back to, after a long hiatus, the excellent book Aesthetics: Problems in the Philosophy of Criticism by Monroe C. Beardsley. In his chapter on Critical Evaluation he uses two useful terms: "Specific Canons" and "General Canons". These are specific and general principles about defects and merits in art. The word "canon" has two meanings, one used in music since the Middle Ages and one used in Biblical scholarship. The musical one is "a general law, rule, principle, or criterion by which something is judged." The other one is "a collection or list of sacred books accepted as genuine."The Western canon is the body of books, music and art that scholars generally accept as the most important and influential in shaping Western culture. It includes works of fiction, non-fiction, poetry, drama, music, art and sculpture generally perceived as being of major artistic merit and representing the high culture of Europe. Philosopher John Searle suggests that the Western canon can be roughly defined as "a certain Western intellectual tradition that goes from, say, Socrates to Wittgenstein in philosophy, and from Homer to James Joyce in literature".The canon of books, including Western literature and Western philosophy, has perhaps been most stable, although expanding to include more women and minorities, while the canons of music and the visual arts have greatly expanded to cover the Middle Ages and other periods, once largely overlooked. Some examples of newer media such as cinema have attained a precarious position in the canon.There has been an ongoing debate over the nature and status of the canon since at least the 1960s, much of which is rooted in critical theory, feminism, critical race theory, and Marxism. In particular postmodern studies has argued that the body of scholarship is biased, because the main focus traditionally of the academic studies of history and Western culture, has only been on works produced by European men.
An example of the use of the word "canon" in music is the contrapuntal technique known as "canon". "Row, row, row your boat" is an example and the canon or rule there is that the second voice enters after the first phrase of the first voice, on the same pitch. In music there are all sorts of different canons. In the Goldberg Variations, every third variation is a canon. The first one is at the interval of a second, the second at the interval of a third and so on. The "rule" or structural principle changes with each canon.
But it should be clear already that the post-modern critique of the Classical canon in music, like so many other of their critiques, is based on an intellectual sleight of hand: music has never really had a "canon" in the sense of a "list of sacred works". Mind you, this is not for lack of trying for all sorts of purposes: to create an unchanging curriculum for music students, as an aid to marketing artists and performances, in order to simplify the repertoire for teaching purposes or in order to sell books and educational materials to the general public, for ideological reasons, and so on. But all this has always been in considerable tension with the reality which is that there is no canon and never was.
I can't speak for literature in which Shakespeare seems to rule absolutely as Harold Bloom thinks, but in music this kind of synoptic focus is hardly possible. First of all, our repertoire is huge and we have a great number of great composers. There are at least two or three candidates for the position of "Shakespeare" in music: J. S. Bach, W. A. Mozart and Ludwig van Beethoven. Arguments over which one of these is greater have been going on for centuries.
Richard Taruskin, in his Oxford History of Western Music, talked about the difference between the repertory and the canon and how they began to diverge, for ideological reasons, in the 19th century (see pp 665 passim in vol. 3, op. cit.). I'll leave you to investigate his discussion which is quite illuminating as regards why this divergence became so marked in the 20th century. Basically, a "narrative history" concentrates on change, i.e. innovation, so it tends to neglect music written for the "repertoire", that is, simply to be listened to, not to fulfill some historical purpose. One interesting problem with this kind of "narrative history" is that it not only focuses on innovation, but it only focuses on certain kinds of innovation. Schoenberg, because of his twelve-tone theory, was a hugely important figure because his kind of innovations seems almost to have been made specifically to advance the narrative whereas the music of Steve Reich, even though it is perhaps even more innovative, is barely acknowledged because his innovations were mostly in the area of rhythm and meter, aspects of music that were not considered to be of historical importance.
Getting back to Beardsley, restricting the use of the word "canon" to just its meaning as a kind of counterpoint and to specific and general principles about defects and merits in works of art removes the problem of there being an inherent bias in its current use referring to a list of works that are "sacred" or "genuine". That was never a very accurate use in any case.
The repertory is always in flux, composers are growing or declining in popularity, new composers are coming along and fighting for performances, the market and performing conditions are constantly changing as well as are the kinds of ensembles finding work and what they choose to play. For all these reasons, while there is some stability to the repertoire--after all, great pieces of music and the appreciation of them does not change radically from one generation to the next, not usually--it is not a list of Works That Are Sacred, but just the repertoire that is chosen most frequently. Why? Well, not because it was written by Dead White Guys, but simply because it is good.
Therefore, all those pinched post-modern critiques about how the "canon" must be radically changed to include exactly the correct demographic numbers of women composers or simply done away with entirely, are really rather irrelevant, aren't they?
Let's listen to a nice piece from the repertory. Here is a lovely Sonata in D major for violin and continuo by Élisabeth-Claude Jacquet de la Guerre. The performers are Riccardo Masahide Minasi, violin and Salvatore Carchiolo, harpsichord: