Supplemental Type Certificate
An STC is needed for any modifications to any part of an aircraft that is critical to its airworthiness.
An example could be a Cessna 172 with a 180 horsepower conversion. This REALLY needs an STC in order to maintain its airworthiness. This prevents someone for putting any old engine in the aircraft. The STC also covers and insures that all systems related to the engine that will be affected by a change (i.e. Fuel, electrical, etc). This type of STC also includes data that is helpful in amending the weight and balance charts for the aircraft. (very important)
Another example is the installation of a STOL system; this usually changes the airfoil of the wing, especially the leading edge. This will affect takeoff and landing distances, as well as the stall speed as listed in the Pilots Operating Handbook, again very important information.
Another more extreme example is called the Texas Taildragger. This is for the Cessna 150, it will change the landing gear configuration from tricycle to conventional gear, AKA tail wheel. This is normally done to give the propeller more ground clearance by pointing the plane up slightly, useful for dirt and gravel runways. This involves a little more that strapping a bigger engine on, you actually need to move all three of the wheels, and support the weight of the airplane in places that weren’t originally designed to support 1000 pounds.
In order for a Supplemental Type Certificate to be approved, it needs to jump through the hoops that the fine folks at the FAA are holding. Once approved people can start modifying perfectly good airplanes.