The full sentence is, "What on earth is wrong?" It's an exaggerated way of saying "What is wrong?" The listener is evidently so upset that the speaker can't imagine what is causing the upset. The speaker thinks, "What on this earth is so horrible to make this person so upset?"

"What on earth" is just a phrase which means "what". It implies the speaker cannot imagine anything on earth is like what is seen or imagined. "What on earth is that?" "Who on earth would think such a thing?"

As far as I'm concerned, something is wrong,why is wrong ,because everybody think it is wrong !but sometimes, what everybody see is not ture ！ like Galileo Galilei! so nothing in the world is wrong !It just good or bad! for example :someone has dead !I say "he will die after all" every one will look down with me ,am I wrong?No ,I am a true man ,but the time is unfit! So I think nothing in world is wrong! Just good or bad!

It is simply a way of asking you "what is wrong." If someone seems to be making a lot of fuss, (often a child) then someone can say "What on earth's wrong?" to add emphasis to the question, but possibly also to suggest that too much fuss, crying, shouting is being made.