What is the exact reason for this? What should I be using? Where should I be applying it?
There are two reasons; one is that all moving surfaces like the hinge pin should not run dry, but have a VERY thin film of oil/grease to prevent 'galling' or 'pickup' which can occur if things are dry. Secondly - when you clean off the old oil/grease (as you should before replacing with clean fresh) - you take away the microscopic grit, dirt and other contaminants and these are large causes of wear in the long term.
It should go on the moving surfaces where metal moves over metal. I prefer a little grease, but to be fair, oil is probably just as good. The most important thing is to clean off old and apply fresh - like changing the oil in a car.
