In addition to the other explanations, twisting pairs of wires can help eliminate interference when the wire is intended to transmit data. If you encode data as the raw voltage value on a single wire, external electric and/or magnetic activity near the wire can affect this voltage by inducing or cancelling some of the current. But if you instead encode the data as the difference in the voltages of two twisted wires, the pair will both experience more or less alteration of their signal, so the difference will remain (nearly) unaffected by external sources.
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