The pylon turn is a maneuver that dates back to some of the earliest days of flying, the early 1900's. Inevitably, whenever a new form of transportation is developed, the first thing people will want to do with it is race. People raced on foot, they raced on horseback, they raced in chariots, they raced in cars, and they raced in hot air balloons. So of course, when the airplane was developed, people wanted to race those too. Now, simply racing in a straight line from one airfield to another would have been a bit dull (and would require two airfields), so to spice things up a bit courses were designed with a pylon to mark one end, around which the planes would make a U-turn in order to return to the beginning. The pylon turn originated with this type of race.
The pylon turn is a banked turn around a fixed spot on the ground, such as a racing pylon, made so that an imaginary line drawn down the wings remains pointed directly at the fixed spot for the duration of the turn, as though the plane were tethered to that spot. If the bank angle and altitude remain constant, this results in an efficient, circular turn.
In 1955, a Christian missionary and former World War II pilot named Nate Saint discovered that the pylon turn could be used to make contact with an aggressive Indian tribe in a remote jungle in Ecuador. Since the plane orbits a fixed location on the ground, he was able to tie a bucket to a long rope attached to the plane, which would then sit virtually still on the ground as he flew in circles around it. In this bucket he would leave gifts for the tribe, and receive gifts in return. This show of friendship lead to the first peaceful meeting between this tribe and outsiders, which unfortunately ended in the murder of Nate Saint and four other missionaries because the tribe hadn't quite gotten the hang of "peaceful" yet. However the next meeting with missionaries went much better when the tribe realized their mistake, and Nate Saint's son now tours publicly with the very man who killed his father.
Over the years, the pylon turn remained an important flying maneuver, and the technique Nate Saint made famous was used by mail services flying into remote locations with no place to land. Mail could be both dropped off and received in the bucket before being hauled back into the plane. However, just as it was inevitable that people would want to use planes for racing, people eventually discovered that the pylon turn could be used in warfare. In the same way Nate Saint's bucket remained motionless on the ground during a pylon turn, a machine gun mounted to the side of an airplane could remained pointed at a ground target.
Although first demonstrated in the United States in 1926, and France in 1932, this technique saw its first combat use in 1964, during the Vietnam War, with the development of the AC-47 Spooky gunship, a modified C-47 Gooney Bird cargo plane (itself a modified DC-3 passenger plane) with a 7.62 mm gatling gun mounted on its left side. It proved itself remarkably in combat, able to keep its gun trained on a target for an extended period of time rather than simply making strafing runs and having to come around for another pass. Not only that, but it was accurate enough to use in close proximity to friendly troops, something unheard of in air power before. The next generation, the AC-130 Spectre (a modified C-130 Hercules cargo plane), was even more impressive. During the period January 1968 through April 1969, the AC-130 flew less than 4 percent of the total sorties against moving targets, yet claimed over 29 percent of the destroyed and damaged trucks. These incredibly successful gunships ushered in the era of close air support, an invaluable tool to the modern military.
Sources:
http://www.ac-119gunships.com/association/somehistory.htm
http://avstop.com/AC/FlightTraingHandbook/EightsOnPylonsPylonEights.html
http://www.afa.org/magazine/april1999/0499gunships.asp
http://jmm.aaa.net.au/articles/4670.htm
Simulacron3 adds: "I've witnessed the 'cone of fire' from the Spectres, but it's best appreciated in a long-exposure picture. They used to empty the brass cartridges from the gunships with coal shovels." That's rather a lot of bullets.