To send a signal, the LEDs change intensity millions of times per second. This is exactly the same thing that regular wireless routers and AM radios do, except with visible light rather than radio waves.
To further boost the data-carrying capacity, the researchers transmitted the data on three different wavelengths of light: red, blue and green. Each carried 3.5 gigabits per second. To the eye, the three signals just looked like a white light. The light actually flickered, but it was too fast for humans to see.
Germany's Fraunhofer Institute demonstrated LED-based data transmission as well, at speeds up to 3 Gbits/s. Chinese and American teams have also shown that LED transmission and receiving can be done - there's at least one company called Visible Light Communications promoting slower versions of the technology.
As with any new technology there's a down side. One issue with visible light is that it is line-of-sight. Unlike radio waves, light from LEDs doesn't bend around corners easily. Light waves also don't penetrate solids, whereas a wireless router works even in another room. And it won't be easy to make this work in bright sunlight, as the sun would overwhelm the receivers.