Possible Spoilers Ahead: So what is Equilibrium exactly. The film stars Christian Bale, Sean Bean, Taye Diggs, and Emily Watson, and it's a post apocalyptic science fiction film basically in which emotion is outlawed in the future and all forms of material goods that can lead to emotion. In the future the governing body of "father" hopes that by outlawing emotion it will keep the world at peace and avoid further war. To keep emotion in check people take a drug called prozium in daily doses. The law is upheld by the Tetragrammaton. They go out of the city into the "Nethers" to round up and kill "Sense offenders", people that choose to not use the prozium and have emotions. The Tetragrammaton is a group of futuristic police officers so to speak known as Clerics, who are specialized in the art of "gun-kata", a fighting skill that teaches the cleric to maximize his abilities with a loaded gun.
Gun Kata is a fictional gun-fighting martial art discipline that is a significant part of the film. It is based upon the premise that, given the positions of the participants in a gun battle, the trajectories of fire are statistically predictable. By pure memorization of the positions, one can fire at the most likely location of an enemy without aiming at him in the traditional sense of pointing a gun at a specific target. By the same token, the trajectories of incoming fire are also statistically predictable, so by assuming the appropriate stance, one can keep one's body clear of the most likely way of enemy bullets.
The Gun Kata shown in Equilibrium is a hybrid mix of Kurt Wimmer's own style of Gun Kata (which he invented in his backyard) and the martial arts style of the choreographer. They disagreed on the appropriate form of Gun Kata, with Kurt Wimmer advocating a smoother, flowing style and the choreographer supporting a more rigid style. Much of the Gun Kata seen in the film is based on the choreographer's style. Kurt Wimmer's Gun Kata is dispersed sparsely throughout the movie, most notably in the introductory scene with the silhouetted man, played by Wimmer himself, practicing with dual pistols.
As the story of Euilibrium unfolds, the Clerics discover that their is an underground resistance that hopes to allow people to feel again. Cleric john Preston, played by Christian Bale, is asked to infiltrate the Resistance and become their champion so that he can destroy it from within. Instead he realizes that having emotion and "feeling" is a powerful human trait and as he deals with all these new emotions, he decides to fight back against Father himself, and in the end free the people of the city and start the resistance full fold as the movie ends.

If you just want to see a cool slick science fiction film then see Equilibrium. If you have already seen it, then watch it again and spread the word about it. It deserves to be seen.