Well, Frankenstein is the name of the scientist, Victor Frankenstein, whom the book is about. Congratulations – you now know more than the average Joe, who thinks the monster created by the scientist is named Frankenstein.
"The Modern Prometheus" part refers to this story by Ovid (Greek poet operating roughly around the switch from BC to AD) about a Titan named, surprise, Prometheus. This titan makes man out of clay. As in, the first man (this is a creation story). To make a long Greek tale a shorter and in English, Prometheus crafts the man out of clay, but screws up when he steals fire from the Gods for man to have. He’s punished in a ridiculously painful manner. What does this have to do with Frankenstein? Well, there is some interesting talk of fire – check out Symbols, Allegory, and Imagery. We noted that Victor Frankenstein decidedly doesn’t take care of the monster the way Prometheus cared for man. Which could be quite a fine point, depending on how you look at it. It’s probably most illuminating to look at the myth in broader sense. Prometheus crafts man. Victor crafts the monster. Prometheus ends up getting his liver eaten out night after night as punishment. Victor ends up having all his family members killed. Both suffer from "playing God," so to speak.
Another way to look at "Modern Prometheus" is to consider that Immanuel Kant actually coined the term in reference to Ben Franklin. Remember his experiments with electricity? Plus, Franklin – Frankenstein – see the similarity? That’s about as far as we’re going to go for now.