Unlike the VCR of old days, the personal video recorder or the PVR is a processor based application. One big difference is VCR was analog, recording analog TV/video signal on a magnetic tape. The PVR handles digital data and records the digital data stream that is the digital TV/Video signal. The digital TV/Video signal is also a compressed signal. Digital data created out of the digitized video is a few orders more that what the analog signal would have needed. The signal is compressed and the techniques are known as MPEG2 and MPEG4. The current and most efficient compression in the MPEG4 scheme is the H.264 encoding method.
PVRs are able to handle this digital data. A PVR may operate on your PC making it easy to record video on it. It could be part of the set top box that has been provided to you by the cable service operator or the DTH ("Direct to the Home") satellite service operator. It can also be part of the converter box that you need to catch digital TV transmitted over the air now that analog TV is dead!