This is an extremely interesting subject.
In the days before organized track systems, etc., etc., PP was employed to save time & therefore fuel on long range operations...primarily oceanic, but it works over land as well.
Here it is, in a nutshell:
Everybody knows the shortest distance between two points is a straight line...on the earth, this is a great circle straight line, of course. However, when you factor in a changing wind, the straight line course may take *longer* than flying some other way.
If you can arrange the flight path so that you have more favorable winds, you may get there sooner than flying great circle. Such a route is called a *minimum time route* and takes into account the atmosphere's pressure pattern...hence, "PP Navigation."
It's hard to do this without diagrams, but let's take a simple example: You are flying from L. A. to Boston. There is a Low pressure area aloft centered around Denver. There's a High pressure area aloft centered around Chicago. Let's say both areas are pretty intense, so that the winds aloft are significant. ATC permitting, the great circle route would take you generally along the route DEN - ORD - BOS. However, you would encounter severe crosswinds all the way, cutting down groundspeed.
If, however, you could fly something like Flagstaff - Amarillo - Wichita - MKE - BUF, you would be south of the Low and North of the High, and thus have tailwinds all the way! Therefore, although you flew a longer path, you would be airborne less time, saving fuel.
This is a very simplified explanation of the way this works. The military and the airlines actually did this back in the "old days." In fact, probably the people who used this the most were the Zeppelins...when you only have an airspeed of forty knots or so, wind makes a big difference!
If you want a better, very technical explanation, try to get hold of an Air Force manual called "Air Navigation." Some of the aviation bookstores might sell it.
The routes were planned on the ground by meteorologists and give to the crews by dispatch.
There is a way to plan & employ it in flight, but it involves sophisticated radar altimeters...stuff that only the transport planes carried.
A simplified type of PP is called "single heading flying." Believe it or not, there is a way to calculate a single heading which, if held from takeoff to landing, will result in flying the minimum time route...and all you need are the altimeter settings at the departure and destination airports! Barry Schiff's book *The Proficient Pilot* has an article about it.
Enjoy.
. Back in prehistoric days, Nav students in the T-43 (B737) were expected to perform a 3 star fix or a sun line every 30 to 45 minutes, with only the use of a mechanical sextant, celestial almanac, paper, pencil, and watch. 
