So there are many things that affect blood pressure. The rate, rhythm, stretch, and contration force of the heart, the hydration level of the patient, function of kidneys, condition of the vessels (arteries can actually contract and dilate, vessels have one-way valves and rely on muscle contraction to help squeeze blood back to the heart) and the position of the patient (orthostatic hypotension is present in many geriatric patients).
Also, the cuff should be properly sized and positioned, in line with the heart and the extremity should be relaxed. There will be a index mark which should be aligned with the major artery.
Understand when talking about the circulatory system, it is composed of 2 pumps, a low pressure pump and a high pressure pump. The body just places them together to make things easier.
First thing to understand is the top number (systolic) is the systemic resistance to blood flow when the heart contracts. The bottom (diastolic) is the resting pressure exerted against the walls of the circulatory system.
Then you have pulse pressure (S-D=PP).
A very narrow pulse pressure (<30mmHg) is concerning because it indicates your heart isn't functioning properly. There could be a number of causes but the mortality rate is quite high.
A wide pulse pressure indicates (>70mmHg) is concerning because it indicates that the vessels themselves aren't stretching properly. This eventually leads to the heart working too hard and growing to become stronger. Initially this allows it to beat harder, but it grows like a normal muscle and the space inside the heart actually shrinks as the heart grows, forcing the heart to beat harder and harder. Eventually you'll end up with LVH (left ventricular hypertrophy) and the output will be reduced no matter how hard and fast the heart pumps.
If someone is suddenly in a hypertensive crisis and stroke symptoms, it is important not to suddenly significantly drop their blood pressure. The reason is, they may be having a stroke and the hypertension is a protective mechanism to overcome the increased ICP (intra-cranial pressure) and CPP (Cerebral Perfusion Pressure) will be MAP (Mean Arterial Pressure, arguable the most important number to track) - ICP.
Some things to note, the heart receives blood during diastole, so, while most people don't pay attention to DBP, it actually is important.
MAP = [(2 x diastole) + systole] / 3 is actually probably the most important number to track.