Twisted Pair
A twisted pair, as indicated by the name, is composed of two wires, twisted together. They are often used in communication protocols because they reduce the amount of electro-magnetic noise emitted by the cable.
If the cable is in an electromagnetically noisy environment, the twists ensure that, on average, the two wires are the same distance from the noise source, and should be affected the same way by the noise. This will manifest as an identical offset in the wires that can be removed to recover the original signal.
Noise Reduction
An electrical current in a cable generates an electrical field. In a twisted pair, if the second cable is carrying the same signal, but with opposite polarity, it will generate an identical electrical field, but also with opposing polarity.
These two fields should cancel each other out, greatly reducing the amount of noise emitted by the cable.
Crosstalk Reduction
When multiple wires are bundled together in a single cable, the reduced noise reduces the crosstalk, or the current induced in neighbouring wires by the noise emitted by another wire.