Zero Hour refers to a collection of comic books printed in 1994 by DC Comics. The Zero Hour storyline crossed over into virtually every title published by DC Comics and resulted in a complete rebirth of the backstory of the entire DC Universe.
A good precursor to all of this is the Crisis on Infinite Earths node; below is a brief description of Crisis, but the full story is very well described there.
Zero Hour was conceived to explain the logical flaws in the aftermath of the Crisis on Infinite Earths storyline, described in brief below. Crisis on Infinite Earths was a concept developed by the DC editorial staff in order to "shake up" their whole comic book line by merging together all of the various 'incompatible' comic book lines. This was done by postulating that there were an infinite number of universes, and the incompatible storylines were in separate universes; this postulation provided the foundation of the Crisis.
The Crisis on Infinite Earths storyline resolved all of this by essentially destroying all of the other universes and dumping all of the storylines together in one single Earth. The incompatibilties were largely explained by making early World War II era heroes "disappear" from the memories of the people or simply by killing them off (as was done to the second Flash, Barry Allen).
However, this didn't entirely work out. As things settled down from this universe merging, lots of cracks in the continuity of the DC universe began to appear. The first major flaw occurred in the Hawkman series, in which it was clear that there were actually multiple distinct versions of the Hawkman character that wasn't cleared up during the Crisis. A "patch" of sorts appeared here in a short series entitled Hawkworld that offered the explanation that the versions of Hawkman were indeed distinct characters. Yet multiple versions of characters kept popping up in the various comic book series.
To fix this, DC introduced the Zero Hour storyline.
The Zero Hour storyline
This is intended as an overview of the storyline, NOT as an end-all reference. For a true end-all reference, one would have to summarize somewhere around 300 comic book issues.
The story begins with the introduction of a series of time anomalies, which resulted in some truly bizarre effects such as multiple Batmans (drawn in multiple different styles) that simultaneously appear in Gotham City. Eventually, various heroes and villains both from the future and the past start dumping into modern day Earth (the one modern day Earth as created in the Crisis on Infinite Earths storyline). Obviously, someone was disturbing the normal flow of time in the universe.
At this point, the storyline had crossed into every comic line in the DC universe, meaning that every hero was somehow affected by this. Because of this temporal distortion, the difficulties existing from the continuity flaws could now be overlooked.
Eventually, it is revealed that a villain by the name of Extant who is capable of time travel is moving around throughout time, tossing people into modern-day Earth in order to create a future of his own design. Extant is actually the amalgamation of several villains with various reality-altering abilities merged together into one body.
At roughly the same time, Hal Jordan, the former Green Lantern, has gone insane and has killed most of the Green Lantern Corps. as well as the Guardians. His reason for this was the destruction of his home town during the Reign of the Supermen storyline from 1993. After killing most of the Green Lanterns, Hal took their power source and intended to bring back Coast City by altering the timeflow.
When Extant reveals himself, the superheroes on Earth manage to defeat him, but not before Extant in essence rips the flow of time, meaning that the universe will end in the very near future: Zero Hour. When this time arrives, the only person with the capacity to repair the timeline is the rather crazy Hal Jordan (now calling himself Parallax), who then repairs the universe in a way he sees fit, which conveniently eliminates most of the continuity problems.
In this recreated universe, all of the comic book lines started over with issue #0 in the month of August 1994, in which the post-Zero Hour status of each comic book line is clearly laid out.
Is The Series Good?
Define "good." The series is entertaining to those who are deep fans of the DC universe who can comprehend all of the continuity and cross-storyline issues dealt with here. It's also not bad for new fans who basically intend to start reading comics with the #0 issue, not really worrying too much about the series before Zero Hour. For the fans falling somewhere in the middle, though, the entire series is rather confusing.
The complexity of the storyline prevents the series from being truly effective, but in order to truly clean up the continuity holes, the story almost has to be highly complex. It also does effectively do the job that Crisis on Infinite Earths could not do: it truly cleans up the utter mess of continuity of the entire DC universe.
In general, Crisis on Infinite Earths provides a better, more readable story for most fans, while Zero Hour actually does the job that Crisis intends to do in terms of cleaning up the DC universe.
One can look at Zero Hour as the equivalent of using a sledgehammer when perhaps a ball peen hammer might have done the job if wielded deftly. It most definitely does the job that it was intended to do in that it cleaned up the DC universe and made the interrelations of the various storylines more clear, but the sheer heft, intricacy, and force of the storyline is almost too much to deal with on a casual basis.
In that regard, unless you are a storyline completist, it is perhaps best to accept Zero Hour as simply being the reason that most of the seeming conflicts in your favorite comic lines are now irrelevant.