Elphaba (the future Wicked Witch of the West) is the illegitimate daughter of her mother and her mother's lover (the future Wizard of Oz). Her skin is green because of a "green elixer" from the lover that her mother drank.
2- A green drink, usually a mixture of green lollipops and Sprite. Often, the one drinking the mixture is accused of being pregnant, much like the Witch's mother in "Wicked."
3- Something ironically scandalous.
- Have another drink, my dark-eyed beauty
I've got one more night left, here in town
So have another drink of green elixir
And we'll have ourselves a little mixer
Have another swallow, little lady,
And follow me down...
- Did you hear about the Wizard? He apparently is the father of the Wicked Witch of the West! That is so green elixir!