in climbing terms a jug is a big hold. probably named after the container. A jug can be grabbed with the entire hand rather than just the fingertips. It is also known as a bucket.

The importance of the jug on the route is that due to it's large size many diferent forearm, arm and shoulder muscle groups can be used to hold on to it with. Usually only a few of these muscles are being used to exhaustion on a climb. When you reach a jug you can transfer you weight around and in so doing can rest the muscle groups which are near to failure. This is called shaking out the pump.

Often a climber will be heard to mutter "where's the jug, where's the jug where's the fucking jug" just before they fall off the route.