A Piggy Back controller is a device that "piggybacks" on top of the ECU. Piggybacks intercept signals coming from the engine and alter them before they reach the ECU.
The most commonly abused piggyback controllers are the Apexi SAFC, VAFC, SAFC2 and VAFC2.
The Greddy E-Manage is a big badass piggyback controller on steroids.
You could think of a lot of the garbage that comes with a JRSC kit as a piggyback, as their relay and crap setup causes bogus sensor values to be passed to the ECU.