The twisting is to prevent crosstalk between pairs of wires.
In fact, one of the main differences between Cat5 and Cat3 cable is avoidance of crosstalk and other interference. Cat5 is much more tightly twisted than Cat3, and the twists are more tightly controlled to be uniform in distance
Crosstalk is an issue whereby signals traveling along one pair of wires interfere with those on another. The more twists per inch of cabling, the less susceptible the wiring is to both EMI and crosstalk.