The Centipede's Dilemma is a way of confusing someone who was self-taught.
The original story goes that a centipede was about to consume a spider when the spider asked for a final question. The centipede said, "Sure, but then I will eat you."
"How do you keep all those legs coordinated?" the spider asked.
The centipede replied, "I don't know. I'd never thought about it before."
At this point, the spider ran off, and the centipede tried to give chase, but was unable to because he couldn't make his legs walk properly, and he could never move again.
Basically, then, the Centipede's Dilemma is just forcing someone to think about in steps
what they have been doing intuitively
, rendering them unable to perform the task in question.
It is most famously applied in a Callahan's Crosstime Saloon story where an amoral but stupid man was using an unusual psychic power to win games, do well as a fisherman, and steal booze from others in the bar. He was found out, and Doc Webster asked him how he did it, which rendered him unable to use the power.
I myself have found it of occasional use, particularly when it comes to people that have beginner's luck. The mental barrier thus generated, though, is hardly a permanent thing, though it was depicted that way above. In addition, it is worthwhile to remember that it only really works with things that people self-taught; if someone else had to teach them the steps involved, they'll be able to break it down to those steps.