It’s a verb innit, and it’s what I’m doing right now.
Its root word is the noun “vigil” which is defined as 1. “a watch kept during normal sleeping hours” or 2. “the act or period of observing; surveillance.”
Therefore, to invigilate someone or something is to keep an watchful eye on it. The word is used particularly to describe the act of observing people taking exams.
Several interesting words rhyme with invigilate, thusly:
Is is necessary,
Though it does not,
So be wary,
And do concentrate.