When a manufacturer develops and sells a car, they program or map the engine to perform efficiently across all possible environments the vehicle may be sold in. They factor in different grades of fuel which may be used, to extreme cold or heat in some places of the World. Even differing emission laws can play a part in how the engine is set up to run when it leaves the factory. The manufacturer also likes to keep well within the known operating limits of the engine, to ensure reliability.
Remapping your ECU involves removing the original map and uploading a new optimised map, this new map will optimise throttle response, air and fuel mixture, boost pressure and more, to give your vehicle the map it was originally intended to have before the manufacturer placed in the compromises. this in effect gives the vehicle more torque and power and a higher MPG.