I can't give you a textbook definition, but it's from greek/roman mythology. A female spirit that inspires one,tfor example the muse of music,poetry,ect-I know they had specific names. In more general terms I've heard writers talk about being inspired by the muse,or having writer's block and needing a muse.
Since my daughter liked the poetry muse i did for a swap,I had to promise I'd make her one. She loves the kid's book Miss Alanius, so she asked for the muse of miscellaneous things.Which is why she has a cape covered in doodads.