The principle with wrapping exhaust piping is that you keep the kinetic energy (heat) of the exhaust gas in the piping rather than having it heat soak the pipe radiating outwards. This keeps the exhaust gas moving as fast as possible, thus helping to eliminate back pressure even further and creating a quasi-scavenging effect at the exducer of the turbo.
All of this means quicker spool and more power potential.
The other obvious benefit is less heat radiating into the rest of the engine bay which would then heat soak everything else. The more the heat of the exhaust gas is aloud to radiate into the piping and outwards further, the slower the exhaust gas will flow. When the wrap is applied properly, you can see up to a 70% reduction in radiant heat.
Similar effects can be seen on naturally aspirated cars as well and it's been dyno tested many times. (I'll try to find some graphs) Many people won't see gains when doing this on bikes, however, because the changes to the flow of exhaust gas usually requires that you re-jet the carbs afterwards, so there are more changes involved than the wrapping alone so it's dificult to gauge finite benefits.
On bikes, because the exhaust is usually routed right next to the rider's legs, the thermal insulation properties can help prevent injury to the rider as well.
I quite literally noticed an increase in power going from a non-wrapped downpipe and test pipe on my Evo to having wrapped both with no other change to the car. I don't recall the last time I had my butt dyno recalibrated, but driving that car every day, you knew when something was different, and I legitimately felt a change. There seemed to be an increase in power, and there was less resonance from under the floor of the car and the exhaust note out of the tip seemed a little louder.
Ceramic coatings like Jet-Hot and SwainTech do the same exact thing, just in a different way. The coatings also keep the heat inside the piping rather than letting it radiate outwards, but there are different coatings for different applications.
If you put a 800 degree coating on a turbo manifold, though it might seem to be rated high enough and works fine for a naturally aspirated application, it will begin flaking off after only a couple runs. You need 1200+ degree coatings for turbo applications, and even those are iffy at best sometimes in terms of longevity. I have seen 1200 degree Swain-tech coatings (arguably the best) flake off too.
The principle behind the wrapped intake is similar. Keep the intake pipe insulated so that the cool(er) air being picked up at the filter behind the bumper grill isn't heated up by the pipe as it nears the turbo inlet.
Gold thermal radiant foil has the same affect but to a much higher degree as gold is the most heat reflective metal on Earth. Many race cars use sheets of it to laminate the firewall to prevent radiant engine heat from entering the cabin. I've seen it used on intakes and intercooler piping too, but the photos are on another computer.
If you were to try to do the intercooler piping, you would only want to insulate the cold side / up pipe as this is where the cool air needs to be kept as cool as possible. On the hot / discharge side, you
don't want to insulate the hot air before it goes into the intercooler. If anything, you would want to use a thermal dispersant coating to try to cool the air before it goes into the intercooler. You don't want to keep it hot.
Doing both the intake and the exhaust, though, the exhaust gas is kept hot and flowing as fast as possible and it is prevented from radiating into the engine bay, and on the intake side, the now limited radiant heat from within the engine bay isn't able to heat soak the intake pipe, so the intake air is as cool as possible going into the turbo.
Many people argue that wrapping can lead to corrosion on the piping due to water being trapped in the wrap, but this arguement hasn't ever been proven from what I have seen, except in the cases of mild steel or aluminized steel piping having been wrapped.
If you're working with stainless steel piping, little to nothing is going to happen. I laugh at the idea that the wrap "traps" water and causes the piping to rust. The piping is still going get hot, and the wrap heats up with it, so any water that touches it is still going to evaporate almost immediately anyway, so there won't be any long term negative effects from water corrosion. The quality of the metal plays a bigger part in corrosion than the wrap itself.
The exhaust on my Evo was wrapped for over two years, and everything looked just as good as the day I wrapped it. (
Yes, I checked it before selling the car.) The exhaust was polished stainless steel, however.
Here is a DIY guide for wrapping an exhaust on a bike. The same exhaust methods are used for a car exhaust.
http://www.crfsonly.com/howto/header-wrap/installing-header-wrap.php