what are they and what do they do?

 

Imagine a garden hose bent in sharp angles through and around some fence posts. Turn the faucet up real high and imagine how the water would travel through it and how much resistance you'd experience from the bends. Then imagine a hose twice as thick, with perfectly smooth, gradual bends, and how much more water can get through the hose.

TL exhaust manifolds are better than most but headers are much less restrictive. Headers are a direct replacement for the stiock exhaust manifold coming off the engine block. More importantly, when you install headers, you probably replace the catalytic converter with a high flow one and replace the cat back exhaust with bigger, less restrictive pipes and mufflers. Yes, with all these mods, you'll likely be throatier, or even down right raspy, but that reduction in back pressure translates to faster revs and more volume of air coming through. More out means more room to get in. So you increase the air flow (air and fuel in and exhaust out) through the engine.

The short answer, horsepower. Freeing up your exhaust is the single most important performance modification you can do. In fact, most other mods depend on it.