As others have said, the wrap keeps the heat in the exhaust. This can improve performance as Apriliarider said, and will keep underhood/rider temps down (since the heat is staying in the exhaust instead of radiating out to the surrounding air). However, it can cause problems too. It doesn't allow the metal exhaust to radiate as much heat out, so the exhaust pipes themselves experience hotter temps, which can lead to problems with the metal. The wrap can absorb liquids; with water this can mean rust, with coolant or oil this can mean a fire hazard. A lot of the cafe racers probably do it more for appearance than any noticeable function.
They also have ceramic coatings that do the same thing.
http://www.jet-hot.com/ is one example. They can be applied to the outside of your exhaust to act like the wraps, without actually having fabric wrapped around your exhaust. However, the ceramic coatings can also be applied to the inside of the exhaust as well. This keeps the heat in the exhaust gas and out of the exhaust pipe itself. Instead of the thermal barrier being between the exhaust pipe and the atmosphere, the barrier is between the exhaust gas and the exhaust pipe. This results in the exhaust pipes themselves seeing lower temps, despite the exhaust gas staying hotter. This also helps keep corrosive crap in the exhaust gases from even touching the metal at all.
Here's a blurb from a Car Craft comparison that I posted on the SyTy board in '02:
August 2002 Car Craft said:
Jet-Hot points out that realizing the full anti-corrosion benefits of header coatings requires coating the headers on their inside as well as outside surfaces. Not all competitors coat the inside surfaces which isn't good because exhaust gases themselves contain corrosive compounds. If the inside isn't coated, the header eventually rusts through from the inside out.
Coating only the outside can also cause another problem: Mild steel tubing fatigues when it gets too hot. An outer-only thermal barrier blocks the heat from radiating through the exterior metal surface while the lack of an inner barrier exposes the metal to added "trapped" heat. In a scenario reminiscent of that caused by the dreaded "curse of the mummified headers" (outer cloth wraps used by some racers), the result can be literal disintegration of the mild-steel tubing.
As for performance, the painted headers were 524°, while ceramic coated were 201°. There wasn't much difference in dyno readings, but they had the engine mounted on a stand, not in an engine compartment, plus there were huge circulation fans nearby.