There isn't an epigraph to Middlemarch, but there is a "Prelude" to the story, so we'll think about that here. (You can read the Prelude here.) Eliot spends a couple of pages on Saint Theresa, a Catholic saint who lived in the early 1500s in Avila, Spain. What's that about? Well, Theresa, according to Eliot, was destined for great things because she had such a lofty, idealistic nature. Even at age seven, Theresa was so gung-ho about Catholicism that she ran away from home with her little brother to try and convert the Muslim Moors in Spain or die trying. But their uncle caught them before they made it very far, so Theresa had to satisfy herself with reforming the way Catholicism was practiced by nuns in Spain.
Eliot points out that there have been many, many Theresas born since then – women who, like Saint Theresa, have lofty, idealistic natures, who want nothing more than to lead epic lives and do great things, but who are thwarted by mundane, everyday concerns (like uncles who don't think seven-year-olds should be missionaries). Women like this spend their lives yearning to accomplish some epic, "long-remembered deed," but end up getting married and having babies and being forced to content themselves with playing the conventional role of wife and mother.
This is an important lead-in to the rest of the novel, because Dorothea Brooke, we quickly learn, is just such a woman. She's a "latter-day Saint Theresa" – someone who yearns to do something amazing and make the world a better place, but who just can't get past the feeling that she was born in the wrong moment for great deeds. From her perspective, no one gets martyred anymore in the 19th century, and her more pragmatic friends and family laugh at her deep and heartfelt desire to reform the world.