(covers information from several alternate timelines)
An agonizer was a small device worn on the belts of Imperial personnel in the mirror universe, used to inflict pain for minor transgressions. More severe offenses called for using the agony booth. (TOS: "Mirror, Mirror")
In DS9: "Shattered Mirror", agonizers were seen as still being used in the mirror universe. They were sufficiently improved over the earlier model that they no longer needed physical contact with their victims to be effective.
In the TNG-era novel Dark Mirror by Diane Duane, a 24th century Empire had incorporated the agonizer into the Starfleet insignia pins worn on the uniform, much as in the primary universe, Starfleet had incorporated communicators. As with those seen in "Shattered Mirror" they were improved technologically, but it was so they could be smaller, and they still needed to touch their victims to work.
Klingon agonizers were also seen in use in the Star Trek newspaper comic strip.