Before nursing, "prioritization" to me meant figuring out what needs to be done first, second, and third with the assumption that the point was to get the most important things done first but that there would be enough time to get everything done eventually. However, in many situations, the reality is that the person CAN'T get everything done in the time allotted. Thus priorizing ensures that the MOST IMPORTANT things get done at all, not just that they get done before other things... because you might run out of time.
I say this because it seems we often hear the advice "prioritize" when someone is asking how to get more done or to work faster. But no matter how well you prioritize, there is still just as much to do and it will still take as much to do everything. Yes, you can learn to bunch certain tasks together for efficiency, but that's not prioritizing, that's being more efficient. You can learn to do certain things faster (assess a patient, hang an IV), but again that's not prioritizing, that's learning how to do things faster (which often comes with experience, which takes time to build up).
Prioritizing ensures that medications get given even if the linen change gets put off. Prioritizing ensures that the unstable patient gets assessed frequently even if another patient never gets the coffee they wanted. Of course, the nurse should make sure the linen gets changed and the patients' requests get taken care of, but not at the cost of patient safety. THAT to me is "prioritization."
In nursingspeak, however, "prioritization" and "time management" often seem to be the catch-all words for the speed and judgement that can only be gained through experience that allows for nurses to get more done than seems humanly possible if you break it down task by task.