Before the invention of magnetic videotape, the only way to preserve a live broadcast for posterity, or re-airing to areas outside of antenna reach, was the creation of a kinescope. These were simply films taken of a monitor playing a live broadcast, and they were of poor quality. In the early to mid-1950s, several companies were working on better TV recording methods. Bing Crosby Enterprises, RCA and a company called Ampex all came up with working methods. The latter had the best quality, so Ampex machines, created in 1956, became the standard. The invention of videotape recording technology not only allowed for a much better method of preserving TV programs for archiving or re-airing, but eliminated the necessity for shows to air live at all. Programs could be delayed for better-timed viewing in different time zones, and content could be taped outside of broadcast studios more easily.
Production of TV on film was possible as well, and was done to some extent, notably starting with "I Love Lucy," but film production was slower and more costly than tape. Early videotape recorders were too large for easy portability, but as they became smaller, they became a practical replacement for film in the news industry. Video also made instant replay possible during sporting and news broadcasts.
In the mid-1970s, videotape also made its way into our homes in the form of video cassette recorders (VCR) and VHS and Betamax tapes. These were two competing formats put out by JVC and Sony, respectively. VHS won the battle and became the in-home VCR standard. These players and tapes freed viewers from having to be home for broadcasts, just as the early introduction of tape freed networks from certain filming locations. It also gave us the ability to buy or rent movies (and later TV shows) to watch at will. The availability of increasingly smaller and inexpensive video cameras has also made it possible for people to make their own video content, more cheaply and easily than on film.
As is always the way, videotape and VCRs have made way for better technologies, such as digital video recorders (DVRs) that allow you to save programs to a hard drive, and DVDs, which can be used to make recordings of programs that will last much longer than magnetic tape. But videotape was the granddaddy of mainstream in-home recording.