This little section almost needs to be considered along with turbos, , because the two typically go hand-in-hand. When gas gets hot, it gets less dense. Less dense means less resistance to flow. It figures, then, that people who are looking at every tiny minutae of performance would want to wrap their exhaust headers. Why? Well exhaust gas exits the combustion chamber extremely hot (duh!) but it cools rapidly as it travels through the exhaust system. In doing so, two things happen. First, the gas becomes more dense and begins to resist flow, and second, as it does this, it disperses heat into the metal exhaust pipes, which in turn radiate the heat into the engine bay, raising the under-hood temperatures. The problem with the gas cooling down is obvious - it begins to slow down and provide resistance in the exhaust system. The problem with the under-hood temperatures going up is that it makes it more difficult for the engine to get a good, cold charge of air. (Colder air is more dense, which means better, more powerful combustion.) This is why you sometimes see vented hoods on cars; they're designed to let the hot air out and keep the under-hood temperatures down. So wrapping the exhaust headers with exhaust wrap helps because it basically insulates the metal exhaust pipes. This means they retain the heat better which in turn means the exhaust gas remains less dense and keeps up it's high flow rate. For turbos, this is a good thing because it means the exhaust reaching the turbo is travelling faster, which means the turbo spins faster, which means more air forced into the engine. Everything is connected, you see? So the ideal system would be a turbo, with wrapped exhaust headers, a vented hood, a cold-air unduction and an intercooler. That combination, whilst expensive, will give the coldest (and thus densest) fuel-air charge into the engine, whilst insulating the exhaust and ventilating the engine bay at the same time.
It's worth pointing out that not all exhaust wraps are made equal. If the wrap insulates too well, then the exhaust pipes get too hot and that can cause all it's own problems from engine bay fires to structural failure of the exhaust or turbo.
It's worth pointing out that not all exhaust wraps are made equal. If the wrap insulates too well, then the exhaust pipes get too hot and that can cause all it's own problems from engine bay fires to structural failure of the exhaust or turbo.