Mirah is one of those girls who has the power to inspire the people around her, and we see her work her magic, even if she doesn't intend to, on more than one character in Daniel Deronda. When Daniel meets Mirah, he doesn't just become inspired to find her family for her; he also inadvertently becomes interested in learning more about Judaism, and in the process starts to learn more about himself than he ever expected to before.
Of course, in the most traditional sense, muses are known for their ability to inspire artists. Hans's relationship with Mirah is a prime example of the traditional muse/artist relationship. At first, he wishes merely to paint her – she's a perfect model for Berenice, the young Jewish woman who fell in love with Titus and whose story Hans wants to turn into a series of paintings. Unsurprisingly, in the process of painting her, Hans falls head over heels for Mirah.