This is the Roman Imperial Standard of the Byzantine Empire (AD 330-1453). The crown with the cross at the top surmounting the double-headed Imperial Eagle represents the authority of the God-anointed Emperor, who ruled with the Orthodox Church’s blessing; the double-headed eagle itself represents the symphonia/harmonia/cooperatio of the Orthodox Church and the Imperial State, governing and leading the Empire in tandem, one in politics, the other in religion. The eagle on the left, holding the sword in its talons, represents the Imperial State led by the Emperor, and the eagle on the left, holding the imperial orb and cross, represents the Imperial Orthodox Church led by the Patriarch of Constantinople.
According to A.V. Soloviev’s 1935 “Les emblèmes héraldiques de Byzance et les Slaves”, (Seminarium Kondakovianum), the interpretation of the tetragrammic “BB BB” emblem’s symbolism is as follows: The two traditional readings of the four “B”s, Βασιλεὺς βασιλέων βασιλεύων βασιλεύουσιν and Βασιλεὺς βασιλέων βασιλεύοντων βασιλεύει (both meaning “King of Kings ruling over the kings/rulers”) were demonstrated by the Greek archaeologist and numismatist Ioannis Svoronos to be later interpretations by the 17th-century historian Marcus Vulson de la Colombière. Svoronos himself proposed three alternate readings: Σταυρὲ βασιλέως βασιλέων βασιλεῖ βοήθει (“Cross of the King of Kings aid the emperor”), Σταυρὲ βασιλέως βασιλέων βασιλευούσῃ βοήθει (“Cross of the King of Kings aid the ruling city [Constantinople]”), and Σταυρὲ βασιλέως βασιλέων βασιλεύων βασίλευε.
As you can recognise, this symbol did not die with the fall of Constantinople in May 1453, but was adopted by many Orthodox states positing themselves as the successor states to Byzantium; most notably, Imperial Russia (1547-1917, Russian Empire 1721-1917) as well as Serbia, Montenegro, the Holy Roman Empire, etc. Here is a magnificent gold double-headed eagle in the former Russian Imperial capital of Saint Petersburg: