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A Turing machine is a device which can respond via some communication medium (like a computer console) in a way that can convince a live human being that it (the machine) is human itself, or at least sentient. Put another way if you hold a conversation with computer and you're thinking to yourself, "Gee I'm sure I'm talking to a real human being." that computer has passed the Turing test and is a Turing machine.
Adapted and developed from a deleted RationalWiki article