The New method creates a new instance of an IAppBuilder. This is needed to create a tree structure in your processing, rather than a linear pipeline. The new instance share the same Properties, but will be created with a new, empty middleware list. To create a tangent pipeline you would first call New, followed by several calls to Use on the new builder, ending with a call to Build on the new builder. The return value from Build will be the entry-point to your tangent pipeline. This entry-point may now be added to the main pipeline as an argument to a switching middleware, which will either call the tangent pipeline or the "next app", based on something in the request. That said - all of that work is typically hidden by a middleware like Map, which will do that for you.
