VCR is Video Cassette Recorder
DVR is Digital Video Recorder
NVR is Network Video Recorder 

VCR is the oldest type of recorder of the 3 whereas DVR is more recent and NVR is the latest as of 2008. VCR records video images on a tape cassette and the tape runs from one end to the other in a fixed sequence.  We will have to go through the beginning to the end to search for a video frame taken at a specific instant. 

DVR uses a computer hard disk for recording.  Hard disk allows random access (or against serial access) and fast retrieval of specified images. Hard disk is also cheap as it is a standard PC product.

NVR refers to an open standard computer as the recording device instead of a proprietary or closed design box as for DVR.  All open standard computers have network interface that is IP compliant.  Therefore NVR is normally refer to as part of a full (end to end) IP based surveillance system.