Mesmerizing is the power to control a person through eye contact. This power seems to be channeled solely through the user's eyes, placing those that they make eye contact with under a trance where they are compelled to obey the user's commands. The users of this power are known as mesmerists.
The user's eyes will glow when this power is in effect and their target's eyes will dilate as they go under the trance. It appears that the target might not remember that they were mesmerized, unless they are already aware of the power of the mesmerist. A mesmerist can mesmerize someone to react in a specific way when they encounter certain circumstances, even if the mesmerist isn't nearby, as seen from when Lucy was compelled to do Alastor's bidding simply by reading text messages.
A target can resist commands or break themselves out of the trance by causing themselves pain, a technique that Julia Wagner employed to protect herself from her ex-husband, Alastor. According to the Book of Shadows, only the mesmerist can unmesmerize their victims.