The depth of knowledge required probably hinges on the examiner's knowledge of the subject. This is especially so when it comes to written exams. In overworked, underpaid government departments, the examiner may not have a clue how VOR works, and is solely relying on key words or phrases he/she has on his/her official checklist. He/she may want to hear/read that the VOR signal is made up of two components with certain characteristics, that the ground station is aligned with local magnetic north (and you need a functioning compass system amongst other things on your aircraft to effectively interpret the ground station signals), etc, etc.
He/she may want to know how crosswinds affect navigation towards ADF stations Vs VOR stations. He/she may want you to know about VOR's limitations (effective range of signals, why there aren't many VOR's in high latitudes, etc). He/she may need you to know what an aircaft VOR antenna looks like and where it is located (so that if you see a broken one on your walkaround, you know what to call it in the maintenance logbook) .
If your intention is to become a pilot, then I doubt that he/she will ask you to draw a comprehensive block diagram of a VOR receiver (They usually reserve that sort of punishment for Licenced Aircraft Engineers
).
Hope this helps.
Cheers.
Q.