What does it mean by "down" in "The system is down at the moment."?

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here down means "not working"

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The precise meaning in this context is 'temporarily out of order', being in an inactive or inoperative state'. 

In your example mentiong 'system' refers mostly to computer systems as Eliot mentioned,otherwise it concerns generators and machines in general as well.

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down = not working; not functioning
up = in working order; working; functioning

It is used mainly in computer systems.

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In Australia it means that the computer system or some other system has failed and is temporarily out of order.