Nice addition to the service, which is now called simply Amazon Video. Sam Machkovech has more information over at Ars Technica:
Once you start watching a downloaded video offline—which can be downloaded in one of three quality settings—the app will pop up a warning that the video will stop working 72 hours after the viewing first began. Simply reloading the app once you’ve returned to an Internet connection will restart any such timers. In a neat twist, offline videos also come with Amazon’s IMDB-fueled “X-Ray” blurbs that can be tapped at any time, meaning you don’t have to get online to answer pesky “who is that actor” questions. However, the app doesn’t include any way to parse how much space you’ve used by downloading videos, nor does it warn you how much space remains. You’ll have to go through your iOS or Android device’s space menus to sort that stuff out.
While it may have originated as a perk bundled with Amazon Prime, Amazon continues to slowly improve their on-demand video service.