Nothing really. Long story short, WWII Longchamp in France ended up with a bunch of pipes that were very popular with GIs. For one reason or another (some debate reasons), they ended up with a lot of pipes and a lot of leather. Someone came up with the idea of leathered pipes and they became very fashionable, again a lot due to US GI popularity. Longchamp eventually got out of the pipe business and stayed with the leather and today Longchamp is a hugely prestigious leather/bags/etc. house in Paris that sells really, really high class, expensive goods. No more pipes though.
It does feel good in its own way, and certainly insulates a hot pipe to the touch, whether that's a good or a bad thing. Some have said the leather covered shoddy briar, but after looking into things, I don't think that was usually the case. They got out of the whole pipe thing in the '70s, I think, though some companies have put out their own leathers since, including Savenilli, I believe.
Mine smokes very well. Has a fairly unique look and, like I said, a nice feel. As far as smoking-specific function, no, it doesn't really seem to serve a purpose.