Specifically, via the TiVo iOS app, recorded content from a TiVo Roamio or Premiere DVR can be played on Apple TV via AirPlay through an iOS device connected on the same network.
This marks the first time that TiVo content can be accessed via a third-party device. TiVo said the integration provides users with a "truly multiscreen experience."
Additional details from the announcement:
When launching a streaming session from the..TiVo iOS app, users can now simply enable AirPlay through the iOS control center, select Apple TV from the menu and toggle the “mirroring” button. Once the device image is duplicated or “mirrored,” TiVo users can view content from their favorite TV shows and movies on an Apple TV seamlessly.