These go by different names at different schools, but a grad student has to pass an oral exam, roughly at the end of their coursework and beginning of their dissertation phase. Sometimes called "orals," "comprehensive exams," etc.
By tradition, they can ask you anything. But in practice, they're not out to kill you. I went to a second tier university, and it was generally believed that the questions at a top school tended to be harder. I have no recollection of mine.
At this time, you also typically present a proposal for your thesis project. Passage of these hurdles makes you a "candidate," i.e., a candidate for a PhD upon defense of your thesis.
"Prelim" also sometimes refers to an exam taken shortly after entering a PhD program to ensure you belong there.
One of the grad schools I attended had both a written "prelim" in year 1 and an oral "qual" in year 2/3. The other just had an oral "general" in year 2.
By tradition, they can ask you anything. But in practice, they're not out to kill you. I went to a second tier university, and it was generally believed that the questions at a top school tended to be harder. I have no recollection of mine.
At this time, you also typically present a proposal for your thesis project. Passage of these hurdles makes you a "candidate," i.e., a candidate for a PhD upon defense of your thesis.