One explaination that I found helpufl was from Paul Graham
"In implementors' terms, a continuation is basically a program
counter and a copy of the stack. You can invoke it like a
function, and you're back where you were when the continuation
was made. So you can return multiple times out the same code.
It's not bad form to use the same continuation more than once.
That happens when you use continuations to do nondeterministic
search, for example.
Another thing continuations are useful for is server-based
apps, strangely enough. We used them extensively in Viaweb
to fake subroutine-like behavior, though because we were
using CL rather than Scheme we used fake continuations made
out of closures."
"To be civilized is to deny one's nature."
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