Stands for "Digital Video Recorder."
A DVR is a device that can digitally record, save, and play back television programs. A DVR can also pause live TV by constantly recording a buffer of live programming as it airs. Later, the user can choose to fast forward (often during commercials) to return to live television.
Most satellite and cable TV companies offer DVR capabilities in one of two forms — local DVR using hard drives or solid-state drives built into tuner boxes, or cloud DVR that records and stores video on a remote server. Streaming TV services like YouTubeTV only offer cloud DVR since they don't provide any hardware boxes. You can schedule DVR recordings using the program guide — simply browse or search through listings and select programs you'd like to record. Once the shows are recorded, they'll appear in a list you can access at any time to watch on demand.
TiVo produced the first dedicated DVR devices that could record and pause live TV. TiVo devices perform the same functions as a DVR offered directly from a cable or satellite provider but are available as a one-time purchase instead of a monthly rental. Some TiVo devices can function as cable boxes using a cable card provided by the cable company, while others can record over-the-air TV using an antenna (without a cable or satellite subscription at all). While TiVo users who buy their own TiVo boxes may avoid the monthly rental fees from their cable company, they must still pay a monthly fee for program listings if they want to schedule recordings.