It's a throwback to the first kilts, the great kilts. They were basically wool blankets belted around the waist and pleated in the back to use up excess material. The extra wool above the belt was wrapped around the upper half of the body and secured with a brooch, often over the shoulder.

In the 18th century, tailors began to remove the top half of the kilt, leaving the lower half (this is what most of us wear). For a fashion statement, some people would take big pieces of tartan and attach it to their shoulders to mimic the original form of the kilt.

These days its mostly worn just for very formal occasions.