Starting with the rope clipped-into a climbing harness, wrap coils of the rope over the shoulder and diagonally across the body. The coil is then wrapped with a bight of rope which is attached to the harness using a carabiner. The final clipped-knot needs to be strong enough to hold a fall, since the "actual" attachment of the rope to the harness can no longer take any weight.
The alpine coil is often used by the lead climber in a group which is walking over flat ground. When climbing steeper ground, the lead climber needs a lot more rope (typically half the coil) to climb to a safe position before bringing up the rest of the group.