PVR or Personal Video Recorder is a consumer electronic device commonly used to record video in digital format on to a hard disk, flash drive or other electronic media.
After recording the video, it can be played back from the PVR or copied on to another digital device or storage. PVR devices include certain set-top boxes, portable media players, camcorders etc.
You can think of them as the next generation of VCRs that record data in digital format rather analog, and have a ton of other extra features.
The term DVR (Digital Video Recorder) is often used interchangeably with PVR.