When an important project or paper is due for school you suddenly become violently ill and skip the class.
They start out with skipping just the class that the paper/project is due in, and slowly move on to one or two periods and then a day, once they've done it a few times they usually start to plan ahead and miss a day before the paper or project is due for convincing.
It is similar to hooky but not really because when someone is "Nick-Sick" they take the time they gain from skipping school or class to work on their paper or project and gain an unfair advantage from the extra time.
Student1: Man i was up till 2 a.m. finishing my senior paper.
Student2: Yeah me too it was hard thankfully its due today and we don't have to worry about it any more.
Student1: Wheres "student3"?
Student2: I don't know the bastard is probably Nick-Sick
After it is known that someone is frequently Nick-Sick
Student1: Whats due today?
Student2: Dunno, Must be something big, student3 isn't here today
Student1: Wheres student3?
Student2: Paper due 3rd period
Student3: Ah, of course