A sarcastic saying used when a person tells another person of something mildly unfortunate that has happened to them, sometimes exaggerated in order to gain sympathy. It implies that the person speaking of their misfortune expects someone to come in playing the saddest song in the world on the worlds smallest violin to correspond with the apparent tradgedy of the situation. Sometimes the person saying this will mime playing a small violin, or try and imitate the sound of a violin.
Jade: Hello, how are you?
Laurel: I just stepped in dog poop and my new shoes got ruined and my feet smell like dog poop, and-
Jade: -Shh... hear that? i'm playing the world's saddest song on the world's smallest violin (mimes playing small violin)
When someone is whining and you are tired of hearing it, you can play the world's smallest violin to provide musical ambiance to dramatize their annoying whine. This is accomplished by rubbing your index finger and thumb together and saying, "This is the world's smallest violin, and it's playing just for you."
Joshua: "America would be so much better if we were a communist country. Everyone deserves to have equal wages, we are all people and that is true equality."
Jeffrey (rubbing fingers together): "Do you hear that Joshua? I got the world's smallest violin, and I'm playing it just for you."