Musical instrument, Russian chromatic button accordion.
Also, synonym of the story has been told many times, or old and unfunny joke.
Meaning comes from the joke about mother in law, which was posted on the Internet numerous times, and soon became "bayan" itself . The word has it's own smiley: :||||||||||||:
-User 1: I'll tell you super-funny joke!
-We buried the mother in law and ripped apart two bayans
-User 2: :||||||||||||||||: