The RCA's uses only two wires for each channel, negative and positive, while a balanced interconnect uses three: negative, positive and inverted positive.

In the recieving unit the inverted positive signal is inverted once more, putting it back ito phase. Now there is two positive signals, one with in phase induced noise, and one with out of phase induced noise.

When the two positive signals is combined the out of phase noise cancels out the in phase noise, resulting in a clean signal.