Rotten bottom links, also known as weak link releases are used when fishing in conditions where there is a high probability of getting snagged. To avoid losing all of your rig and terminal tackle, using a rotten bottom link allows you to sacrifice your lead weight by attaching the weight with a weak length of monofilament. If your weight gets snagged you can simply apply enough force to break the weak link, leaving the weight on the sea bed but allowing you to retrieve the rest of your tackle.
The obvious problem with attaching a weight to weak line is that as soon as you cast out, it is going to snap. This is where the rotten bottom link is needed. Tie your main rig line to the rotten bottom link. Tie the weak line from the rotten bottom link to the weight. Then hook the the loop of the weight onto the open crook of the rotten bottom link. Now the force of the weight being cast will go through the main line and when the weight hits the water, it will detach and be held only by the weak link of line which can be snapped should the weight get snagged at any point.
So that's that. You might well still curse your luck upon hitting a dreaded snag but you will be glad you didn't lose your entire rig, thanks to the helpful little rotten bottom link.