I couldn't understand the meaning of have lines crossed in the sentence below:
"We must have had our lines crossed, thank you for checking."
I'd appreciate it if you help me in this order.
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It means there's been miscommunication. The expression began quite literally where the crossing of lines used to occur with telephone calls (see comment below), which resulted in disturbances (odd dial tones, hearing other peoples conversations etc.)
Person 1: I thought we were meeting on the 20th?
Person 2: No, I definitely said the 30th.
Person 1: Sorry, I guess my lines were crossed. The 30th it is.