Torture is the deliberate infliction of pain on someone.
PPC Agents are forbidden from torturing anyone, be they Mary Sues or other Agents; however, this has not always been an impediment, and both Sues and Agents have been tortured in the past. The former usually leads to a reprimand from the Flowers, while the latter tends to end with expulsion of someone from HQ.
OFUs teach through torture, but in their case, it is called "Learning through pain".
The Disturbing Acts of Violence Department takes care of badfic that contain torture. The DIS tended to torture Agents, one of several reasons that they were despised. Fittingly, some of them ended up being tortured themselves, most notably Twp'atwt (though this is only implied).