When you take a big exam like the SAT or the ACT, an invigilator supervises, making sure everyone keeps their eyes on their own papers and letting you know when your allotted time is up.
Another word for an invigilator is a proctor, though it's mostly used in British English. Aspiring law school students who take the LSAT usually have a professional invigilator whose job it is to monitor the testing room and keep an eye on the clock. When you take a math test, your teacher likely plays the role of invigilator, gathering any stray smartphones and patrolling the rows of desks if she hears any whispering. The Latin root invigilare means "watch over."