UMD Video
UMD Video is a format somewhat similar to DVD, but it has a different menu system, which as far as I know has not been reverse engineered. And of course different discs and encoding - they play 720x480 h264 video with ATRAC3+ audio.
You need to install a PSP firmware of version 2.71 or higher for it to work, see [/docs/]
However, from PPSSPP 1.21 (and current development builds), PPSSPP can run the PSP's own firmware, including its UMD Video player. Run the XMB, use Insert UMD on the pause screen to put the UMD Video image in the drive, and play it from the Video column. Or just launch the video directly, which will do this for you.
For more information about the UMD format variants, see Universal Media Disc on Wikipedia.