What behind this obscure title? Just a web programming paradigm which is very nice and enhances greatly the way of developping web applications. It is also another way of thinking, the consequence being maybe a difficulty for many to integrate the concepts behind this expression of Continuation programming.
I could obviously paraphrase some articles to explain you the meaning, but I prefer to unroute you towards this good explanation : Continuations for Curmudgeons.
There are some frameworks based on this - Seaside (Smalltalk), Borges (Ruby) and SISCWeb (Scheme) being examples. You also can find continuation in java with the RIFE/continuation project (web+continuation).
I let you discover quietly the concept and I wish you a good continuation.