What is severity and priority of a defect, and how do they differ? Can one be high while the other is low?

Severity of a defect reflects the degree of impact the error has on the system's operation — how critical its presence is for functionality.

Priority determines the order of fixing the defect from a business or project perspective — how urgently the error needs to be addressed.

The difference is that severity is a technical assessment of impact, while priority is a managerial assessment of urgency.

Yes, it can happen that severity is high but priority is low, for example, a serious error in a rarely used feature that can be postponed for fixing. Conversely, low severity but high priority — for example, a cosmetic bug on the main page of a website before an important release.