Rented or purchased videos are called 'Flex View' because you can watch them from any four devices, as well as your FiOS set-top box; similar to authorizing other computers for your iTunes media.
You can download movies directly to your device for viewing, or you can remotely download movies to your FiOS box at home. You can then transfer downloaded content to your mobile device, and take your movies with you.
At the moment, FiOS On Demand is only available for the following devices: HTC Imagio, Samsung Omnia II, BlackBerry Storm2, Motorola DROID X & DROID 2, and Windows Mobile 6.5 devices. Don't fret, Verizon assures us they will be adding new devices regularly.
source: Verizon Wireless via Engadget