Inspiration is an unconscious burst of creativity in a the arts or other endeavors. — Wikipedia
Who knows where inspiration comes from. Perhaps it arises from desperation. Perhaps it comes from the flukes of the universe, the kindness of the muses. — Amy Tan, A Small Drop of Ink: A Collection of Inspirational and Moving Quotations of the Ages
The Greeks believed that inspiration or “enthusiasm” came from the Muses, as well as the gods Apollo and Dionysus. Similarly, in the Ancient Norse religions, inspiration derives from the gods, such as Odin. — Wikipedia
Muse, in Greco-Roman religion and mythology, any of a group of sister goddesses of obscure but ancient origin, the chief centre of whose cult was Mount Helicon in Boeotia, Greece. They were born in Pieria, at the foot of Mount Olympus. Very little is known of their cult, but they had a festival every four years at Thespiae, near Helicon, and a contest (Museia), presumably—or at least at first—in singing and playing. They probably were originally the patron goddesses of poets (who in early times were also musicians, providing their own accompaniments), although later their range was extended to include all liberal arts and sciences—hence, their connection with such institutions as the Museum (Mouseion, seat of the Muses) at Alexandria, Egypt. There were nine Muses as early as Homer’s Odyssey, and Homer invokes either a Muse or the Muses collectively from time to time. Probably, to begin with, the Muses were one of those vague collections of deities, undifferentiated within the group, which are characteristic of certain, probably early, strata of Greek religion. — Encyclopædia Britannica
Inspiration is not the exclusive privilege of poets or artists. There is, there has been, there will always be a certain group of people whom inspiration visits. It’s made up of all those who’ve consciously chosen their calling and do their job with love and imagination. It may include doctors, teachers, gardeners — I could list a hundred more professions. Their work becomes one continuous adventure as long as they manage to keep discovering new challenges in it. Difficulties and setbacks never quell their curiosity. A swarm of new questions emerges from every problem that they solve. Whatever inspiration is, it’s born from a continuous “I don’t know.” — Wislawa Szymborska, The Poet and the World, Nobel lecture
I invented something called The Oxford Muse. The Muses were women in mythology. They did not teach or require to be worshiped, but they were a source of inspiration. They taught you how to cultivate your emotions through the different arts in order to reach a higher plane. What is lacking now, I believe, is somewhere you can get that stimulation not information, but stimulation where you can meet just that person, or findjust that situation, which will give you the idea of invention, of carrying out some project which interests you, and show how it can become a project of interest to other people. — Theodore Zeldin, Oxford Muse Foundation
Here are links to pages about closely related subjects.