In the play "Faust I" the poodle transforms before Faust's eyes until Mephisto (a devil) stands before him in the costume of a travelling scholar. This prompts Faust to exclaim in amazement, " Das also war des Pudels Kern!".
Today, the expression is often used when something comes to light that was not obvious until then.
Today's meaning of "des Pudels Kern" : the true facts, the solution;
this quotation is quite often used