Invigilate means to watch over the administration of a test to ensure that no cheating occurs.You won't see invigilate used often but when you do, think about bubbling answer sheets and keeping your eyes on your own paper.
Don't confuse this word with interrogate. The two words sound similar but occupy different grammatical positions within a sentence. You interrogate a person, meaning you ask them questions, but you invigilate a test, meaning you watch its administration. You don't invigilate a test-taker, even if they are the ones whom you, as a test's invigilator, want to interrogate when your suspicions of cheating are aroused. The word derives from the Latin vigilare, which means "to watch over."