Madame Morrible has no counterpart in the L Frank Baum series or the 1939 film. She is initially Head Shiztress at Shiz University, but bites and scratches her way to working directly under the Wizard of Oz. She starts out as a rather genial, if not terribly sympathetic character, but (like the Wizard) quickly falls under the category of Villain. In fact, she is probably more villainish than the Wizard himself.
SusanHilferty.com says that her costumes get more and more elaborate throughout the show.
...At the outset, she appears benign, and she's first seen wearing a rust dress that makes her seem a bit like a nutty professor. But as her ambition grows, her look changes radically. "You see her being revealed for her wickedness," says Hilferty. "For Morrible, I looked at pictures of Queen Elizabeth I, whose clothes made her look like something from another planet. Her hair was pushed way back on her forehead. That's how Morrible appears at the end. Her forehead is tight and hard. The front of her bodice has so much beading on it that it's like a plate of armour. She has high collars that cut off her head, so her face seems to be pushed forward like a plate."
First Day At Shiz: The first dress we see her in is sort of a cross between a kimono and a stereotypical Edwardian gown. It's tagged as "Shiztress"
Emerald City Dress: This could be confusing, because we see her in the Emerald City twice, but this is the dress she wears when she meets Glinda and Elphaba. It's a bright shade of green with gold accents, and very heavily beaded and embroidered. It is tagged as "Press Secretary"
Politician Dress: This is the dress she wears during Thank Goodness, when Glinda announces her "surprise" engagement. It looks like a huge boa. Or possibly she killed and ate a Muppet. It is tagged as "boa"
Mandarin Dress: And this is her final costume. She's come a long way from the simple Shiztress, hasn't she? It is tagged as "boa".