Evil Cycle (悪周期 Warui Shuuki ) or Wicked Phase is a terminology describing a demon (or in some instances a person) when their stress reaches a critical point.
Demons have a tendency to commit acts of violence and sadism when their stress level reaches its limit. This loss of reason reduces their inhibitions and limits, allowing them to use their abilities to a greater degree.
Wicked Phase greatly enhances the user's magical prowess, though their sense of reason drops and it burns their mana quickly. If the user has trained enough for it, they can trigger a Wicked Phase at any time without being stressed. Wicked Phases are commonly associated with a Return to the Origin, where the affected person acts as wild and destructive as a primordial demon. 
Wicked Phase can be intentionally toggled using specially-made drugs and antidotes, generally to train someone for activating it without the drugs.
While there are methods to bring someone out of an Evil Cycle, prevention tends to be easier than stopping it. The Demon World is full of various leisure activities such as playing video games, participating in sport activities, and watching Akudol concerts-- these allow demons to release their stress and return to normal..
Alternatively, extensive conditioning allows one to have a safeword; a specific word or phrase that, when spoken, allows the demon to immediately break themselves out of the Wicked Phase. While effective, this method relies on having a partner who knows the safeword and their ability to use it at the right time, particularly when using the Wicked Phase for combat. 
Iruma's "Evil Cycle"
Even though Iruma isn't a demon, it is noted that with Alicred's power, he is capable of achieving a state similar to that of an Evil Cycle despite being a normal human. In this state, Iruma becomes much less inhibited (though still retaining a core that cares about other people and his classmates).