If someone in authority lets you off a task or duty, they give you permission not to do it. In those days they didn't let you off work to go home very often
If you let off an explosive or a gun, you explode or fire it. A resident of his neighbourhood had let off fireworks to celebrate the Revolution
If you let someone off, you give them a lighter punishment than they expect or no punishment at all. Because he was a Christian, the judge let him off When police realised who he was, they asked for an autograph and let him off with a warning