What does the serbian eagle mean?

The Serbian Eagle is a two headed eagle under a Serbian Crown. It represents the dual sovereignty of the Serbian King over the Serbian Orthodox Church and the Kingdom. This demonstrates that their is no separation of church and state. The Serbian King is the head of both. The Serbian Nemanjić dynasty used the white version as their own to signify their own independence of, and indeed, claim to the imperial throne of Constantinople. The white eagle was retained by most Serbian medieval dynasties, as well as the Karađorđević, Obrenović and Petrović-Njegoš houses and remains to this day in use in the coat-of-arms of all Serbian lands, Serbia, Montenegro, & Republika Srpska.