The muses were nine sister goddesses who in ancient Greece were credited with the inspiration for learning and the arts. They include muses of history, comedy, tragedy, music and dancing: Clio, Thalia, Melpomene, Euterpe and Terpsichore, respectively. Cosimo Tura's 'Allegorical Figure' is likely to have been intended as one of them.
An appeal to a muse would be to a specific muse, rather than for general inspiration. By extension a museum is a place where objects pertaining to the arts and learning are kept.