Like any form of kata it is a type of hand-to-hand combat. In this case, its a fictional fighting form from the movie Equilibrium. According to the movie gunkata is based on scientific analysis of bullet trajectory and range which can accurately gauge the possible mathematical outcomes of a gunfight. In short, it teaches its practitioners how to kickass using only firearms at any distance.
(Quoted from Equilibrium)
DuPont: "The gunkatas. Through analysis of thousands of recorded gunfights, the Cleric has determined that the geometric distribution of antagonists in any gun battle is a statistically predictable element. The gunkata treats the gun as a total weapon, each fluid position representing a maximum kill zone, inflicting maximum damage on the maximum number of opponents while keeping the defender clear of the statistically traditional trajectories of return fire. By the rote mastery of this art, your firing efficiency will rise by no less than 120%. The difference of a 63% increase to lethal proficiency makes the master of the gunkatas an adversary not to be taken lightly."