At a high level, Limelight allows allows you to stream your full collection of Steam games from your powerful Windows desktop to your other PCs and mobile devices. Limelight was started at MHacks 2013 and is currently supported for Android and PC. During MHacks 2014, we added preliminary support for iOS and Windows Phone.
Limelight is an open source implementation of NVIDIA's GameStream, as used by the NVIDIA Shield. http://en.wikipedia.org/wiki/Steam_(software)