Only a handful of devices supported in initial release
Brining its Android offering up to parity with the iOS version, Roku has just updated its app to enable local video playback from your phone to your Roku box on select devices. After signing in and pairing the Roku app with a Roku box (running software version 5.1 or later), you'll now have a new option to select "Videos" from the "Play on Roku" menu in the app. Now all together you can display music, photos or videos directly from your device to the Roku with just a tap.
The functionality seems to work pretty well, but Roku recommends having at least an 802.11n Wifi router for the best performance. Right at this moment the video playback functionality is available on the Roku 3, Roku 2, Roku LT, Roku HD on the set-top box side, and the Galaxy S3, Galaxy S4, Nexus 4, HTC One, and Nexus 7 (2012) on the Android side.
Grab the latest version of the Roku app from the Play Store link above and give it a try for yourself.