Caprice \c(a)-pri-ce, cap-rice\ as a girl's name is pronounced ka-PREESE. It is of English, French and Italian origin, and the meaning of Caprice is "whimsical, playful". From Italian "capriccio" which originally referred to a feeling of horror causing the hair to stand on end (in Italian "capo riccio", meaning "hedgehog head"). The word later became associated with Italian "capra", referring to the goat, an animal whose sudden changes in direction and jumps indicate capriciousness. Also hence the musical term.
For more information, see also the related name Kapri.