A Muse refers to one of seven sisters in Greek mythology, each of whom were responsible for a particular branch of art or science. It was typical for epics such as Homer's Odyssey and Milton's Paradise Lost to begin with an appeal to the "Muse" to help them and inspire them to write their works, and this is something that Pope does as part of creating this mock epic, or a piece that contains the ingredients of an epic but not the subject matter.
Note how the quote makes this mock epic status of the poem clear. This quote comes from the end of the poem, and talks about the fate of Belinda's lock of hair and how it became a star that will be remembered forever. Such an august object it has become that the Muse who inspired Pope to write this mock epic will transform it into a star so that it will be remembered forever:
The Lock, the Muse shall consecrate to Fame,
And mid'st the Stars inscribe Belinda's name!
The Muse is supposedly the agent that Pope therefore appeals to for inspiration and who makes Belinda' hair immortal. Clearly, this is a mock epic because in legends it was only characters who suffered greatly or earnt immortality by overcoming massive challenges who became immortalised in the stars. That such a trivial object as a lock of hair is turned into a star indicates the purpose of Pope's poem: he is poking fun at those who gave to the event much more importance than it actually warranted. The reference to the Muse, a figure associated with proper epic poems, supports this overblown and deliberately exaggerated approach.