No wonder I couldn't find what it was used for! This is the answer from a Badge Expert:
"Great badge!-shame about the condition –from the net :::
The 1911 Festival of Empire, a great exposition in which all of the overseas dominions of the British Commonwealth took part, was held in conjunction with the coronation of King George V. The Festival took place at Crystal Palace and the centre of attraction was the Pageant of London, an enormous enterprise. Some 15,000 performers, representing all walks of life, took part, and by the time the pageant had finished its four month run, it had been seen by over four million people.
--Clearly the badge relates to the Dominions –Australia & New Zealand—However the exact purpose of the badge is in question
Maybe the representatives of the Dominions –Australia and New Zealand were given the badges to wear-clearly an unusual item"