The SOAP note is actually not that difficult to understand... though it seems a bit complicated at first. First break the thing down to it's components: S/O/A/P. Each stands for a particular section.
S- Subjective - This is pretty much anything anyone can tell you about the patient. This stuff is all "unmeasurable" because you can't measure it. This includes stuff the patient tells you. I would include pain in this because (for now) we cannot measure pain. If I chop off one of your fingers, I cannot objectively measure the amount of pain you perceive. If there were no witnesses and the patient was completely unresponsive, this section would be quite bare.
O- Objective - This stuff is the measurable, observable, repeatable stuff. Your physical assessment/findings go here, as would vital signs.
A- Assessment - Think of this as a statement of what you think is wrong with the patient. In effect, this is your working diagnosis, based on the stuff you've found in the above, and therefore is what you are treating the patient for.
P- Plan - This is the "how" you intend to treat.
The deeper you get into doing patient assessments further into your education, the above can fill out quite dramatically. The "S" section can include a "review of systems" which details how the patient thinks each body system is doing. The "O" section will eventually have labs, imaging, and so on. The A/P sections therefore become more detailed as they begin to outline problems you've uncovered and how you intend to address each of those.
Why are you being asked to do SOAP notes? Simple: they are found nearly everywhere in healthcare and the better you understand them, the better you'll be able to read them. At all the hospitals I have been to and have been able to read charts of patients I have had care turned over to me, I have read many, many H&P notes and they've all been based on the SOAP note. The exact format may be slightly different, but the basic stuff is there. These notes are ubiquitous, all medical providers understand them. If I didn't have a pre-made template for doing my patient care charting, the SOAP note is how I'd do mine. Yes, they do have their drawbacks, all charting methods do, but at least the SOAP note is universally understood.