The downpipe is the tube that runs down from the turbo. This is where back pressure builds up: the turbine has to push the exhaust gases through a restricted 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 feel most on a turbocharged engine.

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