The character of Madame Morrible is like the Voldemort of Wicked – she's the really, really obviously evil character. Not only is she named with all the subtlety of an anvil, she is also one in a long line of evil headmistresses – like Mrs. Hannigan in Annie or Miss Minchin in The Little Princess. She's definitely not Minerva McGonagall, that's for sure.
Morrible is almost worse than the Wizard. He's arguably deluded, but she's definitely aware of what she's doing and how she's manipulating people for power.
She seemed to take their stunned silent as assent. She looked down on them. That's why she seems so like a fish, Glinda suddenly thought. She hardly ever blinks. (184.108.40.206)
What's up with this fish comparison? Well, it implies that Morrible is cold – she's manipulative, unfeeling, and highly dangerous. A shark might be a better comparison.
We're never entirely sure what Morrible did to the three girls in her recruitment campaign. She cast some sort of spell, but how long-lasting were the effects? And for that matter, what were the effects?
"You're so predictable," said Madame Morrible, sighing. "That's what makes my job so easy. Now girls, bound as you are to an oath of silence, I bid you to go away and think on what I have said.... And if you should choose not to help your country in its hour of need.... " She clasped her hands in a parody of despair. "Well, you are not the only fish in the sea, are you?" (220.127.116.11)
The fish connection returns once again, this time suggesting that the "fishy" Morrible would like to turn the girls into fishes like herself.
It seems that Morrible's actions lead Elphaba to doubt herself and to grow increasingly paranoid over time. Perhaps that's what the manipulative Morrible had in mind all along – she just gave her three would-be "adepts" the tools to destroy themselves if they openly defied her. She may have just let Elphaba's naturally suspicious nature do her dirty work for her. She even suggests something along these lines in her recruitment spiel, saying how "predictable" the girls are and how they assume she has more power than she really does (18.104.22.168). But does she have the power they fear she does? We never really know.
At any rate, we're not surprised Elphaba tried to kill this nut. But it's interesting that she fails to kill Morrible twice. Though the first failure possibly prevents Elphaba from going to the "dark side" as it were, the second failure seems to send Elphaba dangerously close to the edge of insanity (and Dorothy ends up pushing her entirely over). Elphaba's failure to ever really take any action against Morrible is thematically important. Ultimately, Elphaba is never able to effectively fight injustice, and in the world of Wicked, injustice wins more often than not.
Morrible isn't just the Big Bad of the book. In fact, we're never quite sure how much power she has and whether or not the Wizard is using her. (Or whether she's using the Wizard, for that matter.) We like to imagine that she and the Wizard constantly try to backstab and one-up each other and have a totally demented relationship. (Like, Jan and Michael on The Office levels of dysfunction.) But that's just us.
Morrible also acts as the book's main feminist figure too, which is very odd. She often spouts off little gems like this:
"At any rate, the Wizard needs some agents. He requires a few generals. In the long run. Some people with managing skills. Some people with gumption. In a word: women." (22.214.171.124-32)
Go figure, Madame Morrible is on board with girl power. It just goes to show that decent ideas can come from awful people and vice versa.