As the VCR became a widespread fixture in Japanese homes, the Japanese anime industry grew to behemoth proportions. Demand for anime was massive, so much so that consumers would willingly go directly to video stores to buy new animation outright.
As a result, many series were produced with an intent to go directly to video. While "direct-to-video" became a pejorative in America for works that could not make it onto TV or movie screens, in Japan the demand was so great that direct-to-video became a necessity. Many popular and influential series such as Bubblegum Crisis and Tenchi Muyo were released directly to video as "OVAs."
Although direct-to-video anime had appeared as early as the late 1970s, the first actual OVA series (that was billed as such) was 1983's Dallos, released by Bandai. Other companies were quick to pick up on the idea, and the mid-to-late 1980s saw the market flooded with OVAs. As the Japanese economy worsened in the 1990s, the flood of OVAs drained to a trickle. A few OVAs are still made, but they are now far less common.