By repeatedly trying to make someone miserable you torment them. The noun torment is the result of the verb torment.
After stealing the old lady's purse, you might expect to be tormented by many sleepless nights. Those nights without sleep will torment (tor-MENT) you. They are your torment (TOR-ment). Perhaps you shouldn't have done that. You'll doubtless notice the relationship between torture and torment. But the subtle difference between them is that to torment someone is to torture them repeatedly. Often this is used metaphorically. For example, calling someone over and over to demand payment isn't actually torture, but it's certainly a way to torment them.