The HYDRA of the comic books is basically the evil terrorist equivalent of S.H.I.E.L.D., and is totally unrelated to either Red Skull or the Nazi Party, except by occasional association. HYDRA’s name refers to the mythological creature of Greek lore, as does its motto: “Cut one of our heads off and two more will take its place.” The organization is also known for having resurrected a number of dead characters – Elektra, Spider-Woman, Wolverine, Northstar, and so many more – which were then made to be evil.
The HYDRA of the movie, led by Red Skull, is the advanced weapon technologies and terrorist branch of the Nazi Party; about midway through the film, it essentially becomes a separate entity from the Nazis and altogether autonomous. Thanks, in part, to the discovery of the super advanced Cosmic Cube, HYDRA soldiers are decked out in weapons and tech far beyond that of the 1940s – or even 2011.
Dr. Arnim Zola (Comics)
In the comics, Arnim Zola was a biochemist and one of the first human genetic engineers in history. After being taken in by the Nazi Party, he developed a means to transport one's mental essence into a cloned brain, if need be. In fact, it was with this process that he transferred his own mental essence into a robot body -- equipped with a cloned brain, of course -- so he could live through the decades and into modern times.
Dr. Arnim Zola (Film)
Arnim Zola (Toby Jones) in First Avenger seems far more reluctant to participate in the evils of the Nazi Party than his comic book counterpart, though he's obviously no boyscout either. Zola assists Red Skull in harnessing the power of the Cosmic Cube to create new weapons and technologies for Skull's massive HYDRA armies.
After being apprehended by the Americans, Zola rats out the Red Skull to save his own rear end.
Cosmic Cube (Comics)
In the comics, there are many Cosmic Cubes in existence, all of which have vast reality-warping powers dependent upon the user. Various civilizations and organizations throughout history and the galaxy have developed their own Cosmic Cubes, but all Cubes are embued with the strange, nebulous powers of The Beyonders. Additionally, the Cubes are known to inevitably become sentient beings with certain personality traits passed down from previous users. For example, if the Red Skull were to use a Cosmic Cube -- and he has, though not to any grand success -- that Cube would eventually develop at least some of Skull's personality traits once it became sentient.
Basically, The Cosmic Cube is a terrifying god machine that should probably never be handled by any super villains.
Cosmic Cube (Film)
The Cosmic Cube of the film -- or the "tesserect," as it's referred -- seems to be Asgardian in nature, because it came from Odin's treasure room. However, it's entirely possible that Odin merely obtained the Cube from some other being, as it's unlikely that all the things in his treasure room were made by him.
In First Avenger, the Cosmic Cube is used by the Red Skull and Arnim Zola to equip their HYDRA soldiers with technology and weapons decades ahead of their time. For what purpose, you ask? Well, world domination, of course.
Follow me on Twitter @benandrewmoore.