The series follows the adventures of the Federation starship Voyager during its journey home to Earth, having been stranded tens of thousands of light-years away. In this episode, Captain Janeway must undergo a top secret mission to destroy an element the Federation has deemed too dangerous to be allowed to exist.
Voyager is suddenly rocked by a distant explosion. Although ship systems appear undamaged, all information and control screens are suddenly locked out and replaced by an ominous omega symbol. Captain Janeway arrives on the bridge and informs the crew not to worry. She orders the ship's computer to override the lockout and transfer all sensor data to her ready room, but leaves without explaining to her bemused crew what happened. After locking herself in her office she asks the computer to brief her on the detection of an object, referred to as "Omega". Janeway also summons Seven of Nine to her ready room, as the Borg also have their own knowledge of this "Omega".
Because Voyager has been separated from Starfleet, the Omega Team (a specially trained group which would normally be tasked with handling situations involving "Omega") cannot be brought in to deal with the problem. Janeway decides to break the code of silence involving the symbol and share information with her senior officers. She announces that she has just received the "Omega Directive", an order that requires Starfleet captains to ignore the Prime Directive, regardless of the circumstances, and destroy an object, the Omega Particle, at all costs. As Janeway explains, the particle is very unstable and even the explosion of one particle out in space can nullify subspace for many light years around it, rendering faster-than-light travel impossible within that area.
Moving to the coordinates of the explosion they encounter the planet and its resident alien race that created it. The society is on the brink of economic failure, and are making Omega Particles to "give their children a chance at a future". Seven of Nine, an ex-Borg member of the crew, displays an interest in the scientists' methods, however hoping to save the omega particles and harness them, because she believes them to be perfection - infinite parts working together as one (like the Borg) - despite ample Starfleet and Borg evidence of their incredible danger: The Borg, referring to the Omega Particle as "Article 101", are regardless expected to assimilate it at all costs, even though they have experienced the loss of a large quantity of Borg vessels to Omega Particle explosions while trying to harness the power of the substance. Seven notes, furthermore, that the ability to harness Omega would make the Borg a nigh-unstoppable force; this remark only strengthens the urgency and motivates Janeway to wipe out all Omega particles, at any cost, as determined by the Omega Directive.
Eventually and through a series of issues and difficulties, all the particles are safely gathered together and detonated a safe distance from the alien planet. Just before they are destroyed, they inexplicably stabilize, and Seven is able to view perfection for 3.2 seconds, "an eternity worth".