In the broadest and popular sense, Contemporary music is any music being written in the present day. This could include any kind of present music. However in the strict historical and musicological terminology, the term Contemporary music exclusively refers to the modern forms of art music, this includes:

* The post-1945 modern forms of post-tonal music after the death of Anton Webern (including serial music, electroacoustic music, Concrete music, experimental music, atonal music, minimalist music, etc.)

In a more restricted sense it may only include the most recent forms of this music:

* Contemporary classical music (post-1975) including post-modern music, Spectral music, post-minimalism, sound art, etc.

In the context of popular music, the term contemporary is sometimes used to refer to certain generational trends in music. The pop era of the late 80's early 90's, though contemporary in its day, would no longer be considered contemporary in the 21st century. With the rapid growth of indie labels, the music industry has grown exponentially over the last 5 years introducing genres never before heard of. Thus contemporary music can easily be defined by current market trends.

sources: wikipedia