The concept of continuations is well-established and they have their uses. They have been part of the landscape for years. They can be confusing, and that's impossible to separate from their power.

The inversion of control that this paper is talking about is the way an application running on a webserver typically gets called by the browser rather than the other way around. Continuation-based webservers reverse this inversion and create an illusion of continuity of control flow on the server side. The application is suspended when a page is sent to the browser and resumed (via a continuation) when the response arrives. So this is about permitting server-side applications to be written in a nicer style as far as control flow is concerned.

I think you are getting downvoted because your comment more or less says that you don't know much about the background, and haven't read and understood the paper, but are inclined to dismiss it anyway.