This is a pretty great rundown of the history of continuity changes in the DC comics universe.
Non-nerds may wonder what that sentence means, so I’ll take a swing at a quickie explanation. “Continuity” in superhero comics refers to the overarching story. Each issue isn’t self-contained; they reference prior issues, and not just last month’s. Batman remembers fighting the Joker a year ago and ten years ago, and so forth. He knows he’s been friends with Superman for much of his life. These are just facts in the DC world.
Of course, then you have a problem, because both of those heroes started fighting crime nearly eight decades ago, and yet both are frozen in the prime of life despite having literally decades of experience in their roles — and the storytelling burden of a new issue every month.
(It’s worth nothing that the only other form of storytelling that deals with such long-term continuously published continuity is the soap opera, but there, at least, you’re tied to reality because the actors age in real time.)
Comics address this with two main tools:
First, there’s something called a “ret-con,” which is short for “retroactive continuity.” When this happens, some prior fact in a story is changed, but without upending the whole world. Minor retcons happen all the time; a great “mainstream” example is flashbacks in The Simpsons, since they’re frozen in time in a 20+ year show. When the show started, a memory sequence from 20 years before would unequivocally place Homer in the 1970s, but more modern episodes shift his earlier life forward, right? That’s the kind of retcon.
The other one is the reboot, where massive amounts of prior story and history is jettisoned in favor of a blank-slate renewal with only certain base facts retained. That’s what the linked story is about. DC — the comics company behind Superman and Batman — started in the 1930s, and told stories of a bunch of heroes in addition to Superman, Batman, and Wonder Woman. But in the postwar years, interest in hero comics cratered and nearly all those hero titles (except the big three) were cancelled until a revival in the 1950s. The revival, though, fundamentally changed many of the characters — the original Flash wore a tin hat, for example, but the version resurrected in the 1950s is the one you probably think of when someone says “The Flash”; he’s Barry Allen in a red suit with a cowl and a lightning motif. (In comics, the original era is referred to as the Golden Age, and the 1950s revival is the Silver Age.)
Another excellent example of a reboot is what Abrams did with the 2009 Star Trek film. We see the same characters, and the same ship, but we’re telling new stories with them. The Chris Pine version of Kirk has never met Harvey Mudd, never seen a tribble, and so forth. The inclusion of “regular” Spock in the film gives us a link to the “normal” Trek universe, but it’s otherwise distinct, with its own threads of story and history to unfold, unencumbered by any of the history that’s been piling up since the original series aired.
Anyway, the storytelling problems that surface in comics are unique to the form (though kin to those faced by any long-running narrative universe, including soaps and certain long-running franchises like Star Trek and Doctor Who). This article is a fun exploration of how DC has addressed them in the last eighty years.