Your wittiness is your ability to be clever and make people laugh. If you're known for your wittiness, you'll probably get invited to a lot of parties.
If someone is quick with a joke or a clever comment, you can describe them as witty — and this general characteristic is known as wittiness. Your brother's wittiness makes him popular with his friends, but it may sometimes get him in trouble at school. And the wittiness of the writing might also make an otherwise serious novel much more interesting to read.