Hi Sally. This is called a rain chain and is a nice alternative to a rain leader / downspout. There is a tradition of this sort of thing in Japanese architecture, often with cups along the chain. They can be quite beautiful. The idea is to direct the rainwater down but to slow it down and soften the flow, even to celebrate it. The rock at the bottom also helps break up the flow of rainwater and let it flow gently into the landscape. Here's an example of one with the cups:
EvB Design