It's the name of one of the Greek muses. I think she's the muse of epic poetry (as opposed to other types of poetry.) It is supposed to mean "beautiful voice" (kalli- is used in compounds to mean 'beautiful' and ope is actually a related word to "open" in English, referring to where the voice comes out of. A more literal and also more awkward translation might be "Pretty Throat" or even "Pretty Mouth.")
Calliope makes me think of either the muse or the instrument.