Greek mousa (from which muse derives) is a common noun that means “song” or “poem”. In Pindar, to “carry a mousa” is “to sing a song”. The Muses were, therefore, both the embodiments and sponsors of performed metrical speech: mousike, from which “music” was “the art of the Muses”. In ancient times, before books were common, this was the major form of learning. The first book on astromony, by Thales, was set in dactylic hexameter, as were many works of pre-Soctratic philosophy. Both Plato and the Pythagoreans included philosophy as a sub-species of mousike. Herodotus, whose primary form of delivery was public recitation, named each one of the nine books of his Histories after a different Muse. 
The muses weren’t assigned standardized divisions of poetry and art until late Hellenistic times. The nine canonical Muses include:
Calliope (beautiful of speech)—chief of the Muses and the muse of epic or heroic poetry
Clio (glorious one)—muse of history
Erato (amorous one)—muse of love or erotic poetry, lyrics and marriage songs
Euterpe (well-pleasing)—muse of music and lyric poetry
Melpomene (chanting one)—muse of tragedy
Polyhynmia (singer of many hymns)—muse of sacred song, oratory, lyric, singing and rhetoric Terpishore (one who delights in dance)—muse of choral song and dance
Thalia (blossoming one)—muse of comedy and bucolic poetry
Urania (celestial one)—muse of astronomy
The British poet, Robert Graves, popularized the concept of the Muse-poet in modern times b
ased on pre-12th Century traditions, and medieval troubadours, who celebrated the concept of “courtly love” and the romantic poets (and that’s a whole other post!). Wrote Graves:
“No Muse-poet grows conscious of the Muse except by experience of a woman in whom the Goddess is to some degree resident…A Muse-poet falls in love, absolutely, and his true love is for him the embodiment of the Muse…But the real, perpetually obsessed Muse-poet distinguishes between the Goddess as manifest in the supreme power, glory, wisdom and love of woman, and the individual woman whom the Goddess may make her instrument…The Goddess abides; and perhaps he will again have knowledge of her through his experience of another woman…”
And what about women Muse-poets? Plato coined the term, “the tenth Muse” for these rare specimens (at the time) and it is a term that remains in use today.
But, what is it really? What IS one’s muse? And how can you summon it (when you need it)? I think it’s a personal phenomenon; like one’s belief and relationship with God. So, I can only tell you of my personal experiences and thoughts and what works for me…
Let’s start with the opposite: many writers complain of experiencing writer’s block at some point in their career—that affliction of not accessing one’s creativity, when the muses have all fled to Tahiti or someplace far away and you are left with a blank page or
more importantly—and alarmingly—a blank mind. No desperate search, hot shower, long walk or discussion with a friend will seduce those holidaying muses back. You’re stuck. Here’s my solution: simply let go. Embrace the emptiness … and something wonderful will fill it. We are all vessels, able to carry a diverse and fluid mixture of things. My belief—in fact my conviction—is that God dwells inside each of us, connecting us to the beauty and wonder of nature and to each other through means we need not know. And when I “empty” myself and let my “muse” enter me, I am communicating with God. That simple.
Each of you has felt it: that otherworldly, euphoric wave of “knowing”, of resonating with something that is more than your visible world. Shawn McKim Murphey of Joyous Life Works calls it your “inner spark(le)”: when the hairs on the back of your neck tingle as you write that significant scene…or tremble with giddy energy as you create that perfect line on a painting…or glow with a deep abiding warmth when you defend a principal… or surge in the frisson you share with fellow musicians on that exquisite set piece…or cry out joyously with that cresting orgasm at exactly the same time as your cherished lover. These are all God moments; God’s poetry.
If, indeed God moves us to express that within us which is divine, then poetry is the language of the heart and music is the language of the soul.
I once insisted to a good friend that I don’t—CAN’T—write poetry. I was lying; to myself. I write it all the time, though not formally. We are all poets and we all “write” it, whenever we open ourselves and let our “muse” enter us. Every creative moment is poetry.
That’s not to say that one can’t entice those capricious muses. Here are a few things that help me:
Music: music moves me in inexplicable ways. I use music to inspire my “muse”. Every book I write has its thematic music, which I play while I write and when I drive to and from work (where I do my best plot/theme thinking). I even go so far as to have a musical theme for each character.
Walk: despite what I said above, going for a walk, particularly in a natural environment, uncluttered with human-made distractions, also unclutters the mind and soul. It grounds you back to the simplicity of life, a good place to start.
Cycle: one of my favorite ways to clear my mind is to cycle (I think any form of exercise would suffice); just getting your heart rate up and pumping those endorphins through you soothes the soul and unleashes the brain to freely run the field.
Hope you found this useful.
Recommended Reading:
Robert Graves, The White Goddess, a historical grammar of poetic myth.