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.

When you eat dirt for the first time and leave your family to build a shack in the woods