Most of the music books you'll find on the shelf are about Western music. From the end of the Middle Ages to modern times, composers and performers in western Europe gradually developed widely accepted standards for tuning, melody, harmony, meter , notation, form, counterpoint and other music basics. These rules are a sort of grammar for the language of music. Just as the basic rules for putting together sentences and paragraphs help people understand each other, knowing what to expect from a piece of music helps people understand and like it.
Of course, music, like language, changes through the centuries. A Bach invention, a Brahms symphony, and a Beatles song are different forms in different genres, and at first they may sound as if they have nothing in common. But they all use the same musical "language" and follow basically the same rules. They are all examples of Western music, and are all more like each other than they are like a Navajo lullaby, a Chinese opera, or a west African praise song.
Wherever Europeans went during the colonial era, they took their music with them. So, in places like Australia and the Americas, not only do most of the people speak European languages, much of their music also sounds Western. What are the rules of this European musical language? A complete answer to that question would be long and complex, since Western music, like any living language shared by many different communities, has many "local dialects". The short answer is: Western music is generally tonal , based on major or minor scales, using an equal temperament tuning, in an easy-to-recognize meter , with straightforward rhythms, fairly strict rules on harmony and counterpoint, and not much improvisation. This is, of course, a huge generalization. Twentieth century art music, in particular, was very interested in breaking down or even rejecting these rules.
But because they are flexible enough to allow plenty of interesting but easy-to-grasp music, the rules are still widely used, particularly in popular music. In fact, the use of these traditional rules for Western music is now so widespread that it is sometimes called common practice. They are what makes Western music sound familiar and easy to understand.
Non-Western music is any music that grew out of a different culture or musical tradition than the European. For someone who grew up listening to Western music, Non-Western music will have a recognizably exotic sound. This comes from the use of different tuning systems, different scales, different vocal styles and performance practices, and different approaches to melody and harmony.