iOS 9.3 is coming in the Spring and will introduce Night Shift as well as a number of other new features.
See Handoff on OS X Yosemite and iOS 8 in Action
While Handoff doesn't appear to work reliably at this point in time and is listed as one of the features currently unavailable in the beta software, some users have been able to get it working, giving us a quick glimpse at how the feature works.
A video from French site Mac4Ever displays how the feature works with Maps, Safari, and Mail. A map opened on the iPhone is automatically picked up by the Mac, displayed in the lower left corner of the screen, with the process repeated for a site in Safari and an email message in Mail.
Handoff is also demonstrated in a second video from Cult of Mac, which explains how Handoff works and shows the feature being used with Safari and Mail. The video also demonstrates a second Continuity feature, which allows Macs and iPads to make and answer phone calls relayed through an iPhone.
Handoff, Mac/iPad phone calls, and the other Continuity features will continue to be refined during the iOS 8/OS X Yosemite beta testing period. Both iOS 8 and OS X Yosemite are currently available to developers and are expected to be released to the public in the fall.