Homer is calling on Calliope, the muse of epic poetry, for inspiration in relating both The Odyssey and The Iliad. In Greek mythology there were traditionally nine muses, all females, all daughters of Zeus and Mnemosyne (Memory), and all born to her at the same time. The other muses were Clio, muse of history; Euterpe, muse of flutes and lyric poetry; Thalia, muse of momedy and pastoral poetry; Melpomene, muse of tragedy; Terpsichore, muse of dance; Erato, muse of love poetry; Polyhymnia, muse of sacred poetry; and Urania, muse of astronomy.
Apparently these muses were not merely poetic conceits but minor deities who were actually believed to be real and to be the sources of inspiration in their respective fields. Homer believed that the goddess Calliope was dictating the entire Iliad and Odyssey to him and that he was only reciting what he heard.
There are poets and other creative writers today who still speak of the need for the inspiration of a "muse" in order to to be able to write effectively. It is not hard to relate to such fancies, since most of us feel there are times when we are feeling so inspired that it is as if the words are being dictated to us by an invisible presence, and other times when the "muse does not attend" and we cannot seem to write a decent line or sentence to save our lives.
The brilliant American psychologist Julian Jaynes (1920-1997) published a fascinating book with a rather intimidating title: The Origin of Consciousness in the Breakdown of the Bicameral Mind (c. 1976).
According to Jaynes, ancient people in the bicameral state of mind would have experienced the world in a manner that has some similarities to that of a schizophrenic. Rather than making conscious evaluations in novel or unexpected situations, the person would hallucinate a voice or "god" giving admonitory advice or commands and obey without question: one would not be at all conscious of one's own thought processes per se. Research into "command hallucinations" that often direct the behavior of those labeled schizophrenic, as well as other voice hearers, supports Jaynes's predictions. (Wikipedia)
Although the title of Jaynes' book is intimidating, the text is easy to read and understand because he was an excellent writer who had studied most of the world's greatest writers, often in their own languages. His ideas are controversial but fascinating.
See reference link regarding "Why do mortals need gods help" below.