Medea's killing of her children is symbolic in several ways. First, the boys are a pretty clear representation of Medea and Jason's marriage, as they are the product of what was once a loving relationship. Medea feels like Jason has betrayed and soiled that marriage by taking a new wife, so she's out to destroy every last remnant of it. It's surprising she doesn't burn down the house, too. Instead, Medea satisfies herself with slaughtering her kids in the house where they were born, sacrificing them on the altar of revenge.
As we mentioned in "What's Up With the Ending?", the murder of the sons could also be a symbolic act of feminine revolt. Medea is put upon by the male-dominated society around her – banished by Creon, deserted by her husband. She could be seen as rebelling against the role of mother, in which women were often trapped. There's nothing wrong with being a mother; the problem comes when that's all you're allowed to be. Also, it's probably no coincidence that Medea's final act of revolution is to kill two young boys. You could interpret the murder as the destruction of the next generation of potential oppressors. In the end, the slaughter of Medea's sons seems to be a symbolic act of bloody resistance.