An Excruciator is a device meant to be worn (or perhaps implanted would be a better word) which inundates the recipient's brain with unimaginable pain. It is usually called by the definite article (The Excruciator) rather than the indefinite (An Excruciator) because of its deep historical significance (like The Model-T).
When the Ur-Quan martyr Kzer-Za, for whom the Ur-Quan Kzer-Za name themselves, discovered that pain was the only way to be free of Dnyarri compulsion (thus beginning the Dnyarri Slave Revolt), he inflicted this pain upon himself with acidic poison. This tactic, while greatly successful, had the downside of guaranteeing his death.
Later on in the revolution it was, oddly enough, a black Ur-Quan (later to be known as the Ur-Quan Kohr-Ah) who perfected the Excruciator. The device was non-lethal and the pain it gave to its subject was incredible. For years all Ur-Quan (and assumedly the other races of the Sentient Milieu whom the Ur-Quan liberated) wore this device as the only way to combat the Dnyarri.