The GravityLight uses a sack of sand or stones to gradually pull a piece of rope through a dynamo mechanism which generates electricity to power an LED. It is a cheaper and more sustainable option than a solar powered light, which requires not only a solar panel but also a battery. The product is aimed at the developing world and its makers raised 400,000 dollars at indiegogo.
The technology could be further improved by including pulley mechanisms that were used to operate human powered cranes and lifting devices in pre-industrial times. This would allow a person to lift heavier weights and thus power more powerful lights.
To be precise, the light is not powered by gravity. It is muscle-powered, while gravity stores the energy and fulfills the role of a battery. Hat tip to Bernd Vleugels.