The weapon was designed to draw energy from the Gravity's End proto-universe phenomenon, and use that energy to fire a beam of energy at a predetermined target when conditions in the proto universe were just right. The weapon featured a cloaking device which made it undetectable, and the Big Bang Weapon was deployed near Espoir Station.
In an alternate future timeline, Ies Bredell was able to fire the weapon at Earth, destroying the planet and causing the collapse of the Federation. During the explosion the starship USS Alexander was thrown into a timewarp, which sent it back in time eight days. The USS Enterprise encountered the heavily damaged Alexander, and Captain Lucas Rayner tried to warn the Enterprise what had happened. However the damage inflicted by the Big Bang Weapon and the timewarp was too much, and the Alexander exploded.
The Enterprise then traveled to Espoir Station to investigate the threat. An Elasi frigate commanded by Bivander Zane tried to stop them, but the Enterprise was able to drive the Elasi off. Boarding the station, Captain James T. Kirk, Doctor Leonard McCoy, and Commander Spock were able to free the Enterprise from a tractor beam the station had placed on a starship and captured Bredell. After getting the code to the weapon's control system, Spock decloaked the Big Bang Weapon, and the Enterprise destroyed the weapon with her phasers. (TOS video game: Judgment Rites)