The downpipe is the pipe that runs down from the turbocharger. This is where back pressure builds up: the turbine has to push the exhaust gases through a narrowed section and often a catalytic converter. Enlarging it frees up the turbine, allowing it to build boost earlier and more decisively - it is the exhaust modification you notice most on a turbocharged engine.

What changes behind the wheel: the response. The turbo takes less time to spool up, and the power delivery holds higher in the rev range. On a remapped engine, this is the part that allows the control unit to deliver what it promises; without remapping, the ECU compensates and most of the gain remains untapped.