Mostly double-talk, the roots of the word can be broken down as: super- “above”, cali- “beauty”, fragilistic- “delicate”, expiali- “to atone”, and docious- “educable”. Put together, it roughly means “Atoning for educability through delicate beauty.” In the film itself, it is defined as “something to say when you have nothing to say”.
“The song occurs in the chalk drawing outing animated sequence, just after Mary Poppins wins a horse race. Flush with her victory, she is immediately surrounded by reporters who pepper her with leading questions and they comment that she probably is at a loss for words. Mary disagrees, suggesting that at least one word is appropriate for the situation and begins the song.” (Wikipedia)