The Roku app is great for controlling a Roku set-top box, but that's what you have a remote for, right? The app previously included audio and picture streaming from Android devices, but now it goes one step further. The new update allows Android devices to stream video directly to the player over WiFi.
The 'Play on Roku' tab in the interface has a new entry for videos, which should pull up all the compatible videos on your device organized by folder. Keep in mind the videos have to be in a format your Android device can decode. Just pick the video you want and hit play. It's a little bit like Airplay for Apple devices.
This feature is currently officially supported on the Samsung Galaxy SIII, Samsung Galaxy S4, Nexus 4, HTC One, and Nexus 7 (2012). The app doesn't seem to be checking the device model, though. The video option pops up just fine on a 2013 Nexus 7. The more relevant caveat might be that Android 4.0 or higher is required. You also need a Roku 3, Roku 2, Roku LT, Roku HD, or Roku Streaming Stick. The update should be live for everyone.