Luis's definitions are good. If you talk about "letting myself off the hook", it usually means that you stop blaming yourself for something. "I blamed myself for denting my friend's car. However, after it was determined to be the other driver's fault and the insurance paid the bill, I let myself off the hook." If it is something that a person is obligated to do, they usually don't "let themselves off the hook". He or she is let off the hook by circumstances or somebody else. "You promised to help with the picnic today, but seeing as it's raining, we'll have to cancel it, so I'm letting you off the hook."

It means to "get away with something", that is, to "avoid responsibility for something you've done or promised". "You agreed to drive me downtown today, don't try to get off the hook by using that silly excuse!" ** It may have other meanings, though... **Regards! :D