The pulse pressure is the difference between the systolic blood pressure and the diastolic blood pressure.
PP = SBP -DBP
It is determined by the stroke volume (amount of blood ejected by the heart) and compliance of vessels (the vessels reaction to this bolus of blood).
A higher pulse pressure will be measured in the smaller arteries further from the heart, as the pressure drops and the compliance increases.
Elderly patients that have stiffer vessels with a lower compliance will have a higher pulse pressure, but this isn't the whole story. The pressure wave reflects along the vessels and is reflected more easily by a very stiff vessel (harder vessel has less give, so wave travels faster, less delay, a high pulse wave velocity). Usually the wave reflects and returns during the diastolic phase but when the wave returns earlier it can increase the measured systolic pressure and lower the measured diastolic pressure, overall increasing the pulse pressure. (picture below describes this much better graphically).
PP can be considered an independent prognostic factor for cardiovascular morbidity (and it makes sense as a sort of crude marker of atherosclerosis and arterial stiffness).
Higher PP is proven to be related to smoking, diabetes, dyslipidemia, obesity and power sports activity.
Every 10mmHg increase in PP is associated with an increase in cardiovascular death risk of around 10%. However, also a low PP (below 45mmHg in patients with already advanced heart disease is linked with increased mortaility).
Wide PP for example >80mmHg is almost diagnostic in the case of severe aortic regurgitation.
The value to look for is a peripheral PP over 55-60 mmHg, this should alert you to likelihood of arterial stiffness and increased cardiovascular risk.