“What do I owe you?”

You're going to go to a concert with your friend. Your friend bought the tickets, and now he's giving them to you. You want to know how much they cost, so that you can pay him back. You ask:

What do I owe you?

owe (someone)(an amount of money)

If you "owe (someone)" money, it means that you are supposed to pay that person:

He owes me twenty dollars.

It could be because you borrowed money from them, because you broke something that belonged to them, because you lost a bet, or because you're buying something from them.

What do I owe you?

This is a question that means "How much money do I owe you?" You ask "What do I owe you?" in a casual conversation.