I'm not familiar either, but here they are talking about graduate students [0]. I guess it's a sort of final cumulative exam at the end of the programme.
I mean a final exam at the end of the program covering not just a single subject but potentially anything you studied during the program. But in practice it has to be more restricted, that's why they ask him what he prepared: it could be potentially anything, but to practical reasons they have to restrict it to a few subjects. Still more fields than what is covered by a single course. Or at least this is my interpretation.
I knew what you meant, but as I said, these type of exams are not at the end of a PhD program. At Princeton, it appears that the general exam occurs after year one or two: https://www.math.princeton.edu/graduate/requirements
I went to MIT for a physics doctorate, and in 2009 their generals were done in three parts. Part 1 was given in August of 2009, basically immediately after orientation, so I had spent the entire summer studying for it.