Twist barrel is another name for what is often called a Damascus barrel, that is one made by winding white hot strips of iron and steel around an iron rod (called a mandrel) and welding them together by blows from a hammer. That was done because at the time gun makers had not figured out how to drill a straight hole in something as long as a barrel.
That barrels made that way have inherent weaknesses should be obvious, and it is generally recommended that guns with twist or Damascus barrels not be fired, even with black powder. (Yes, I know some people do fire those guns with black powder loads, and some even fire them with hot Magnum loads and say they have no problems. Some people drive cars with worn tires and bad brakes, too, but I don't recommend it.)