The OVA -- "Original Video Animation" -- was a term applied to serially-produced anime released direct-to-video, a label that came to prominence in the late '80s and '90s. Japan's then-booming economy meant video-rental businesses needed product to fill the shelves, and so scores of animated productions came into being to satisfy that demand. OVA animation budgets were generally larger than their TV-anime counterparts, so many of them were widely acclaimed for both their production values and their more free-ranging storytelling (since you weren't constrained by TV broadcast standards).
After Japan's economy tanked in the 2000s, most anime was either produced theatrically or for TV, since those were the venues where money could still be found to finance production. But the OVA has slowly made a comeback of sorts, thanks in part to some novel financing and distribution methods -- e.g., creating an OVA for theatrical and then a video release.
Because of their generally higher production standards than TV shows, OVAs are great candidates to be reissued on Blu-ray Disc. Earlier OVAs, like Tenchi Muyo!, were shot on film and can benefit from an HD remaster as long as the original film elements are used. More recent productions like Broken Blade or the new Berserk series are all-digital productions done in HD to begin with, and so look excellent on Blu-ray by default.
Check out our suggested list of OVAs on Blu-ray Disc, and feel free to add your own suggestions below.
Image: Broken Blade © Yunosuke Yoshinaga · Flex Comics / BBPC. Image courtesy Sentai Filmworks.