The phrase "world's smallest violin" is part of a common mocking reply to diminish someone's stories of woe or disappointment. As of 204, the world's actual smallest fully functional violin was built in 1973 by Eric Meissner and was 1.6 inches long.
When used as a mocking expression, the phrase "world's smallest violin" is usually accompanied by the person performing a mocking pantomime of playing a tiny violin by rubbing his fingers. The phrase has also appeared in movies and animated programs where characters produce an actual violin from out of nowhere. The phrase is generally invoked when someone feels the problem being discussed is either unimportant or overblown.