One story goes that after having a very heated quarrel, she emptied the contents of a chamber pot on his head and he responded, "After thunder, there generally falls rain". Later in life, apparently Socrates remarried, but in reflecting on Xanthippe, he said, "Marry or marry not; in any case, you'll regret it."
Quite a few works have alluded to Xanthippe, including Shakespeare's Taming of the Shrew. If you want to refer to a woman as a nagging wife with a sharp tongue, you can say she follows the ways of Xanthippe.
I think it's best put by Henry Fielding in his book The History of Tom Jones, where he describes a shrewish woman named Mrs. Partridge:
She was, besides, a profest follower of that noble sect founded by Xantippe of old; by means of which she became more formidable in the school than her husband; for, to confess the truth, he was never master there, or anywhere else, in her presence.-------------------------------------
On a personal note, while I certainly do not consider my wife a Xanthippe, one of the things I liked most about her was her ability to outwit me and to keep me in my place, and she's much funnier than I am. People tend to flatter ministers too much, and we probably like it too much. She's very good at keeping me in my place as I need it.
This is one of those allusions that people might appreciate unless they understand it. You could tell a woman "You remind me of Xanthippe; the wife of Socrates himself!" She might be flattered if she doesn't know any better. I found this entry at the online Urban Dictionary where some girl is rather proud to have an "amazing" name after a woman in ancient Greece.
It's kind of like a few years back when Reebok named one of their womens' shoes after a mythical creature, the Incubus, because the name sounded cool. Then some women started to protest when they learned that Incubus was actually a demon who would go around lying on women in their sleep in order to rape and impregnate them. Hence, it is very important that if you're going to use an allusion, you had better know to whom or to what you're alluding!