NVIDIA G-SYNC aims to reduce screen tearing, stuttering, input lag, and other similar gaming problems by not having the monitor's refresh rate be fixed but rather it's a dynamic refresh rate that will scan out whenever the GPU is finished rendering. That's the short story; more information is available via NVIDIA.com.
Up to now only Windows 7/8/8.1 have supported G-SYNC when using a capable graphics card and monitor/adapter, but that looks to be changing. One could assume that under pressure from Valve with SteamOS / Steam Machines and other Linux gaming initiatives, G-SYNC will ultimately come to Linux, but buried within the 337.12 beta driver are indications the developers might be working on the support right now.
A Phoronix reader tipped me off today to the fact that with the nvidia-settings 337 changes that are open-source, there's references to G-SYNC. In particular, some defines right now related to G-SYNC handling by this Linux GUI utility for managing the NVIDIA binary driver. There's a NV_CTRL_GSYNC_ALLOWED define and the code comment says, "NV_CTRL_GSYNC_ALLOWED - when TRUE, OpenGL will enable G-SYNC when possible; when FALSE, OpenGL will always use a fixed monitor refresh rate." This isn't a shared header file with the NVIDIA Windows driver.
Hopefully an upcoming NVIDIA Linux driver release will unveil the official Linux support for G-SYNC. Within the next driver series, 343.xx, we know there's big changes ahead with NVIDIA dropping pre-Fermi support from their mainline driver and moving it off to a new legacy driver. Stay tuned for more information, or if we have an official comment from NVIDIA, but generally their official statement comes down to not commenting on unreleased Linux driver features.