There are, of course, many kinds of music from nonwestern cultures. They do not all share any particular characteristics -- they can differ from Western music in many ways.
Perhaps the most important difference between Western music and many other kinds of music is the scale that is used. Western music tends to use a scale with 8 tones per octave. This is not dictated by nature -- it is just a convention. There are other ways of creating scales. One well known scale is the pentatonic scale. As its name suggests, it divides the octave up into 5 tones instead of 8. This scale is used, for example, in Japanese music.
This is a major difference between Western and some other traditions of music, but it is not the only one.