The main reason is that
it is cost effective.
This cost effectiveness
breaks down into two reasons. First, the compression works well,
delivering an excellent quality to quantity ratio. In other words,
a song that is one fifth the size it would be on a CD is NOT one
fifth the quality. Second, it is an open standard. That means anyone
can get the specification (it costs 140 USD) and no single company
owns the standard. Also, one can easily get public domain source
code. Furthermore, this has driven to a proliferation of MP3 decoders,
widely available for free.
Additionally, there is an
element of timing--MP3 became available and used at the right time,
during an explosion of file sharing on the internet and the ability
to cheaply market MP3 hardware players. And while the quality is
not as high-fidelity as CDs, most people will accept it.