To be on the hook is to be caught in a bad situation or to owe money. When you’re on the hook, you’re in a tight spot. If you're on the hook for your half of lunch, you better pay up!
Once a fish is on the hook, it's in big trouble — it’s about to become dinner. Similarly, when a person is on the hook, they're in some type of trouble. You could be on the hook to the IRS if you owe them money. Anytime you're on the hook, you're in a bad situation and you should wiggle free, especially if it's just a matter of paying up.