Primaries are evolved human beings with deep connections to time itself. Primaries help time "think." Without Primaries, time would be unable to function.
Primaries evolved over hundreds of thousands of years. Much like how man evolved from earlier primates, time also evolved. Some individuals who evolved alongside time, known as Primaries, are inextricably linked to time. They have the ability to see the changes in time and can keep track of multiple timelines. As a result, Primaries give off the impression of being insane.
Compared to gears in a clock, Primaries are a support system for time. As a result, if Primaries are paradoxed, the structure of time is weakened. If enough Primaries are paradoxed, time will collapse and cease to exist. This is the basis of the Army of the 12 Monkeys' mission. The Messengers are a group of assassins sent back through time to paradox Primaries with knives made of bone from their future selves. Their ultimate goal is to bring about an eternal Red Forest free of the passage of time.
It is important to note that a natural death does not harm time. Only the paradoxing of a Primary will weaken the very structure of time.