The top of your head is called the "crown" of your head (that's where you would wear a crown). So he hit the top of his head when he fell. Broke his crown indicates to me that he cracked the top part of his skull. Ouch.

This rhyme was created in the late 1700s. Needless to say the meaning has been lost in time. It has been said that it is a satirical reference to King Charles I. The crown could mean a head dress like a crown or a pint glass that has line mark that means crown, or the simple answer could be it means head. No one truly knows, or at least I can't find any agreeing references.