FreeSync is the AMD-developed, VESA-adopted standard for Adaptive-Sync similar to NVIDIA's G-Sync that allows for displays to have a variable refresh rate. The goal is for the display's refresh rate to match the GPU's rendering rate on a frame-by-frame basis to eliminate potential tearing or stuttering. Dropping the frame-rate out of performance-sensitive situations can also lead to lower system power use / longer battery life.
Unlike NVIDIA's G-Sync, no specialized hardware is required to support FreeSync. This week at Computex, AMD was showing off the first FreeSync capable monitor that can run between 40Hz and 60Hz. The monitor on display was a retail monitor that can already support FreeSync just via a firmware upgrade. For supported monitors out there right now that have the capability of supporting the variable refresh-rate, it will be up to the vendors to issue new firmware, but that's probably unlikely given they would rather drive new monitor sales with a line-up of official "FreeSync" monitors.
Embedded below is a video of AMD's Computex FreeSync demo courtesy of AnandTech. Sadly for those interested in FreeSync/G-Sync, the current open-source Linux graphics stack will need to see some updates in order to handle this technology, as covered yesterday within the Linux GPU driver global thermo-nuclear war article.