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Even people who know little about technology, have at least a general understanding of what is "possible" given their understanding of the state of technology. Today people are exposed to so much technological advancement that it may be hard to imagine something that technology cannot someday accomplish.
What Clarke was hinting at is something so far beyond what a person believes is possible, given any stretch of technology that they can possibly imagine, that they are incapable of seeing it as anything but "magical," or in essence, "Godlike" power. Don't think of simple mechanical concepts, like moving planets about... think in terms of "willing existence into being" and "sculpting time."
(Never thought I'd be explaining Arthur C. Clarke quotes...)
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