In ancient times, only the great sages and seers were priviledged enough to hear the stories of the mythological demigods (Devatas) and demons (asuras). So, because he wanted to share the Story of Rama with the rest of the world, the Great Sage Valmiki created a script, which we now know as Sanskrit, and recorded the story on stone tablets (similar to those found in ancient Egypt). Because Great Sage Valmiki had the inspiration and desire to share this story with the world, he was called its Muse. In Ancient Greece, they called this person a Rhapsode, as in the case of Homer, who originally recorded the epic poem, the Odyssey. These ancient storytellers were called Bards in Old England, and Reconteurs in Medieval France. Today, this person is called an author, the originator of a written work.
If you were to look at a work of fiction today, you would notice that most have a page dedicated to the author. You might call this page the Introduction to the Author, and you would generally find it at the end of the novel. In ancient times, they called this page the Invocation to the Muse, and they placed it at the very beginning.