The front part of a Subaru turbo-back exhaust is known as the downpipe. The downpipe bolts directly to the turbocharger outlet, and collects exhaust gas from the turbine wheel as well as the wastegate. The wastegate outlet part of the factory Subaru downpipe has one of the worst layouts ever in exhaust-dom, with the wastegate gas running directly into a flat plate. That gas has to somehow find its way over to the main section of the downpipe. It's obviously not a high-flow layout, so upgrading this pipe is great for performance, as well as for preventing "boost creep" (uncontrolled increases in boost) from poor wastegate flow.
The factory downpipe has a pair of catalytic converters in it. Some aftermarket downpipes have a catalytic converter. Some don't. A cat-less downpipe will generally out-flow one with a catalytic converter in it.
It's good to keep at least one cat in the systems for a lot of reasons, one of which is good citizenship and keeping the air clean. Another is that there are two oxygen sensors in the exhaust system, and having a cat between them keeps the ECU happy and not throwing "Check Engine" lights.
Note that the 2010+ Legacy GT, 2014+ Forester XT, and the 2015+ WRX hava a new low-mounted turbo, and they don't have a "downpipe" -- most people call it a "J-pipe" because of its shape, which is sort of like a letter J.
The Invidia downpipe shown above is fitted with a 49-state-legal catalytic converter.
Of course, it is against federal law to remove any working catalytic converter from the car.
Next: Upgraded Top-Mount Intercooler