Medea is an unabashed polemic, meaning that Euripides has some pretty specific opinions and he wasn't afraid to talk about it. The play is still, to this day, one of the most radical texts of feminine revolt in all of Western literature. The first thing Medea does when she goes on stage is list, in extensive detail, all the reasons why it stinks to be a woman. This was a pet theme of Euripides and can be found in many of his plays. Medea, however, stands out as the most uncompromising.
Euripides is also widely considered to be the most "modern" of the ancient tragedians. Evidence of this can be seen in Medea. Yeah, it still uses a chorus, verse, and heightened language, but in comparison to some of the other plays of its time, the play's dialogue sounds quite natural. The characters speak in a much closer approximation of everyday speech than in the plays of Aeschylus and Sophocles.
Euripides is known for having been the first Greek playwright to start exploring the psychologies of characters. This is also a pretty modern concept. Medea is a powerhouse role that's been taken on by many great actresses over the years. The character's emotional pyrotechnics give a lot for an actress to sink her teeth into.
While Euripides's focus on character was often at the expense of a solid plot, it made him really popular with actors. Some scholars believe that is why more of his plays made it through the ages than any other Greek playwright. Actors may have kept the plays around so they could show off their stuff.