Why do headphones have a left and a right speaker?

The left-ear speaker's made for your left ear(and vice-versa) so you can hear better.

Stereo music is mixed with the intention that certain instruments will appear in different locations in the the stereo spread (somewhere between left and right). To accurately recreate the intentions of the music producer, you must put the headphones on for the intended ears. Orchestral music is recorded in stereo with a specific arrangement of instruments on the stage (violins on the left, for example). To recreate the sound as you would hear it from the audience, you must put the earphones on the correct ears.