Only a couple of people have answered this, so I will jump in. Oh, I'm sure there are some others who have asked a similar question, so you can do a search on this forum, but I don't want to be one of those guys who gets somewhat 'rude'.

Anyway, yes, you got it pretty much right. The headers or exhaust manifold are the tubes you see leaving the heads and lead to the up-pipe. There are different types of 'headers' out there. There are 4-2-1 and 4-1, for example. Meaning, four tubes go into two tubes and then into one for the 4-2-1. Without going into detail, these configurations give you different power outputs and different areas of your rev range (due to flow). Also, there are equal length and non-equal length 'headers'. Equal length will give you better power gains over non-equal, but in a WRX, you will lose that boxer sound which many love. Now, whether they are good or not depends on your setup. When you have a turbo, things change a lot in how an exhaust setup helps you. When it comes to the exhaust BEFORE the turbo, you want your exhaust gases to be travelling at a high speed (to spin the exhaust turbine). You also want a lower temperature (also helps speed things up). Technically, putting 'headers' on you car which normally have a larger tubing then stock, you will be slowing down these gases and increasing volume. This isn't really that great for a stock turbo that is small and likes having that fast exhaust gas. With larger turbos, however, having this increased volume can help, especially at higher rpm's. After the turbo, which is where you find the down-pipe, you want to have a free flowing exhaust with little backpressure. Backpressure isn't that great for either the compressor or the turbine of a turbo because it forces these 'wheels' to work harder to get the same output. This can lead to destroyed bearings after a while. Sorry if this doesn't make sense, I'm horrible at explaining things. Try looking at the math of this stuff....yuck!