Well, i am not sure about the american system of fares. But here in india, we have two methods of fare calculation:
1. SLD - Straight Line Distance (Most common)
2. PP (Point-to-point)
Lets say there is a flight which goes Delhi-LHR-Rome. The Delhi-Rome fare will be lower than Delhi-LHR, since it is calculated on SLD.
Then some routes offer PP fares. For eg. Lets suppose, i book a seat on a flight from Madras-Delhi and onwards from Delhi-LHR on a connecting flight, i dont pay the full fare for the 2 flights. The fare is only marginally higher than Madras-LHR direct, and the symbol PP is stamped on your ticket.