A Kiznaiver is a human that had the pain mark engraved on them, thus connecting their minds and bodies. When one Kiznaiver gets hurt, said pain (and an exact copy of the injury) will carry to all other Kiznaivers in the world, no matter the situation the other Kiznaiver is/was in. For example, if one Kiznaiver were to cut his finger while preparing food, all other Kiznaivers would get a cut on the exact same finger the first Kiznaiver got his cut on. The pain of getting a cut would get carried over, too. Once the pain and injury get carried over, the Kiznaiver that is the cause of the injury does not get healed.
The Kiznaiver program was an unfinished attempt at creating world peace. Arguing that if other people could feel other's pain, their will to inflict it on others would decline.