What is so special about an octagon barrel?

Answer

They are cool. Seriously, the octagonal barrel was used by early gunsmiths because it was easier to fabricate, I suppose. Without advanced tooling, it would be difficult to hand-forge a piece of steel into a perfectly round shape.

Most older guns have octagonal barrels, even the first Winchesters made in late 1800's.

--------------------

It's not so much that the tooling would have to be advanced -- lathes have been around since halfway to forever -- but turning a round barrel with a low-speed lathe is immensely labor-intensive; grinding flats into bar stock takes much less time.