Updated models with AMD graphics options expected in early 2017.
Apple Releases Firmware to Activate PowerNap on 2011 MacBook Airs
Apple lists the full capabilities in this Knowledge Base document. Capabilities include getting new Mail, syncing Calendar, Contact and Reminder changes, and more. When plugged into power, your Mac can download software updates and make backups with Time Capsule.
Apple only supports PowerNap on 2011 MacBook Airs and beyond as well as the 2012 Retina MacBook Pro. The capability should move over to more of Apple's laptops as Apple makes a full transition to SSD. Built-in flash storage is listed as one of the requirements of the technology. Apple just released a firmware update that enables this functionality in the 2011 MacBook Airs, while support for the Retina MacBook Pro is said to be "coming soon".