The significance of the double-headed eagle comes from the foundation of the Byzantine Empire by Constantine the Great in 313 AD. In moving the seat of his empire from Rome to Byzantium (promptly renamed Constantinople, which today is Istanbul), he wanted to emphasize that this was both an Eastern and a Western empire. The double-headed eagle, looking both East and West, was designed to symbolize this orientation as well as the Emperor's domination of both religious and secular authority.
Subsequent empires and monarchs adopted this symbol, from the Russian Empire to the Holy Roman Empire, whose continuator was the the Austro-Hungarian Empire. It was also the insignia of the Russian Empire, where our Order was headquartered for many years. The OSJ was an official Order of Nobility of the empire from the reign of Paul I.