Spoilers ahead for the Supergirl episode "Legion of Super-Heroes," which airs tonight.
The Great Disaster is a fictional event which took place on Earth-AD, the home of Kamandi and various other post-apocalyptic heroes and villains from DC lore, created by Jack Kirby.
Taking place sometime between the then-modern DC Universe and the world of Kamandi, The Great Disaster wiped out most civilized life on Earth and in its wake, a race of intelligent animals rose up to subordinate the few remaining humans.
While the tales of Kamandi, the Atomic Knights, OMAC, and other Kirby characters were never officially the canonical future of the DC Universe, versions of the Great Disaster have been told and retold, experimented with and teased, for years.
A popular version of "a" Great Disaster (not necessarily The Great Disaster) was one from which humanity recovered -- but which destroyed most of the world's data, leaving characters from the future (such as Booster Gold and the Legion of Super-Heroes) with only a general idea of what happened in the past. The result was a "void in time," a lengthy period during which historical records were incomplete, inaccurate, or non-existent.
This was used in post-Crisis on Infinite Earths stories as one of a number of ways that DC minimized time travel. The concept of a multiverse had been abandoned, and the sole remaining DC Earth had a timeline that was still being revealed and explored, so characters like Booster Gold could travel out of story necessity, but time travel was not a key part of their ongoing narratives, because it was being discouraged by editorial at the time. Also, once Booster arrived in the 20th Century, he had only partial knowledge of the events that would take place there, and could not simply go around preventing every crisis before it happened.
It is the Void in Time idea (although they do not call it that) that is referenced in tonight's Supergirl, when Mon-El explains that his Legion comrades know almost nothing about the world's past, and what they do know was generally recounted to them by him.
In the comics, this move kept the Legion at arm's length from the rest of the DC Universe even more than they already had been over the years. That distance from the stories that "counted," coupled with the loss of Superboy and Supergirl, contributed to the Legion feeling less like a part of the DC Universe for several years and more like a stand-alone story.
Of course, there was another version of the Great Disaster -- one which was used in the unpopular 2006 event series Countdown to Final Crisis. There, Legion of Super-Heroes member Karate Kid was infected with a sentient super-virus known as Morticoccus, which eventually got loose and created the world of Kamandi on Earth-51. Given the involvement of the Legion of Super-Heroes, one should at least suspect that Morticoccus could play a role going forward...although the fact that it came from Countdown likely means it will not.
Supergirl airs new episodes on Monday nights at 8 p.m. on The CW all throughout January.