It is an important prop. Here's the deal:
Glinda and her friends are getting ready for a party at the Ozdust Ballroom. One of her friends finds a "hideodeous" hat (it's the Witch's hat) which is a present from Glinda's dear ol' gran-gran. Glinda says, "I'd give it away but I don't hate anyone that much." Her friends say, "Yes, you do." So she gives it to Elphaba. At the party, Madame Morrible approaches Glinda and tells her she has been accepted into the sorcery seminar thanks to the efforts of Elphaba. Glinda feels remorse and when Elphaba arrives in the hat, everyone laughs at her. That is when Glinda realizes she must make things right. At that point they become friends. The hat and its consequences are what unite the two. So, yeah, it is pretty important. There's lyrics concerning it and it becomes a plot device.
Sorry if I sound condescending but it's true.
Butters, go buy World of Warcraft, install it on your computer, and join the online sensation before we all murder you.
--Cartman: South Park
ATTENTION FANS: I will be played by James Barbour in the upcoming musical, "BroadwayWorld: The Musical."