An electrical circuit can be thought of as a complete "loop" through which charge can travel. Therefore, it actually has to be physically complete - there can be no openings. That is, the current actually has to have a full path to take.
But there is an exception:
If the supplied voltage is high enough, charge can "jump" an "open circuit." This is clearly a dangerous situation, and one way in which a person can get shocked. Think of the unfortunate situation of sticking your finger (or a paper clip, etc.) into an electrical outlet (or something like a toaster, for that matter). You would "bridge" the circuit, becoming in effect, a resistor.
That's bad.
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