Here is an explanation of its meaning from wikipedia:

Roots of the word have been defined, as Richard Lederer writes in his book Crazy English as follows: super- “above,” cali- “beauty,” fragillistic- “delicate,” expeali- “to atone,” and docious- “educable,” with the sum of these parts signifying roughly “Atoning for educatability through delicate beauty.”[citations needed] This explication of its connotations suits the fictional character of Mary Poppins, in that she presents herself as both superlatively beautiful and also supremely intelligent and capable of great achievements.[citations needed]

There you have it. It is more fun to say (and sing) than it is to worry about what it means.