Continuation

General or introductory materials

Here is a collection of short descriptions, analogies or metaphors, that illustrate this difficult concept, or an aspect of it.

“In computing, a continuation is a representation of the execution state of a program (for example, the call stack) at a certain point in time” (Wikipedia's Continuation).
“At its heart, call/cc is something like the goto instruction (or rather, like a label for a goto instruction); but a Grand High Exalted goto instruction... The point about call/cc is that it is not a static (lexical) goto instruction but a dynamic one“ (David Madore's A page about call/cc)

“Continuations represent the future of a computation, as a function from an intermediate result to the final result“ (Continuation monad section in Jeff Newbern's All About Monads)
“The idea behind CPS is to pass around as a function argument what to do next“ (Yet Another Haskell Tutorial written by Hal Daume III, 4.6 Continuation Passing Style, pp 53-56))

Wikipedia's Continuation is a surprisingly good introductory material on this topic. See also Continuation-passing style.
Yet Another Haskell Tutorial written by Hal Daume III contains a section on continuation passing style (4.6 Continuation Passing Style, pp 53-56)
HaWiki has a page on ContinuationPassingStyle, and some related pages linked from there, too.
David Madore's A page about call/cc describes the concept, and his The Unlambda Programming Language page shows how he implemented this construct in an esoteric functional programming language.