From our Best of YouTube video series we like this one from the London School of Sound on how to coil cables properly. The London School of Sound is a non-profit independent organisation dedicated to teaching professional sound and music production.
The video shows two ways to coil a cable, but before we get to that, you may be asking "why is it wrong to coil a cable around your arm?" There are really two answers to this. The first is that when we're done coiling the cable we want it to hang in a nice coil that can be easily un-coiled and laid out in a nice straight line. The second reason is that we want to avoid damaging the cable. Here's how the damage occurs.
Cables have a natural twist to them due the steps in manufacturing where the interior cable wires or shield/braid have twisting. You can see this twisting in this video. The art of coiling a cable is in allowing the cable to follow its natural twisting so that successive coil rings lay neatly. When the cable is coiled opposite to its natural twist direction it will tend to create knots, which when pulled can turn into kinks (sharp bends) that can cause deform the interior of the cable and cause damage.
So now you know why you want to coil your cables properly, and here's how to do it: