The flying buttress, besides being something one says so they can giggle, was a clever architecture design. The weight of the walls of huge structures like massive cathedrals combined with the roof, many times built with heavy slate shingles, required the walls to be extremely thick to support all of the forces. This made it impossible to add in large windows, particularly stained glass ones, that would allow the light in and to show the rendered scenes completely.
The flying buttress uses a very heavy structure like a pylon as an anchor point and an arching bridge connecting the anchor to the wall that requires support. This design allows the main walls to be constructed thinner than the older fortress-style structures so the stained glass windows will catch the light and allow people to see the entire scene depicted by the artist. The outward force of the wall is transferred through the bridging arch to the anchor, which gives the wall the strength to hold itself and the roof up despite massive weight. The design is so stable that there are hundreds of massive buildings from hundreds of years ago that are still standing today.
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|XXX| |AAAAA|
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X=Supported Wall
B=Bridging Arch
A=Anchor