From the attention he lavishes on telling her story – including an extended interior monologue in Book 7, it is clear that Medea is one of Ovid's favorites among his own characters. (You may be interested to know that he also wrote a tragic play with Medea as the heroine; unfortunately, this play has been lost.) For modern readers, too, it is hard not to be fascinated. Medea is the original "strong woman." If it weren't for the magical help she gives Jason, he would be toast (literally – as a result of tangling with those fire-breathing bulls). Then she does some other cool – and also scary – stuff, like give Jason's father his youth back through a mystical ritual involving throat cutting.
Over time, however, the scary side starts to take over. You can see this in the gruesome revenge she deals out to Jason's uncle, King Pelias, when she tricks his daughters into subjecting him to the rejuvenation treatment, including the throat cutting, but leaving out the part where she heals him with magical herbs. If we were Jason, and our wife had just helped us out in this violent way, we DEFINITELY would not make her mad. But Jason shows himself to be an ungrateful jerk: when Medea gets back, she finds out he's taken a new wife. This time, she goes ballistic – murdering Jason's new wife as well as their children. Then she flies off. The last we see of Medea, she is still in murderous mode: she tries to kill Theseus, then flies off in a cloud of mist when this fails. Did we mention that Medea is the grand-daughter of the Sun-god? Makes sense. If you mess with this lady, you're bound to get burned.