The BBBB is the acronym of the Greek Empire of the Middle Ages, most known by the name Byzantine Empire or, among Western Europeans, as “Imperium Graecorum” (“Empire of the Greeks”). Spanning from year 395, when the old Roman Empire was split into a Western (Latin) Roman Empire and a Eastern (Greek) Roman Empire, until 1453, when the Byzantine Empire’s capital city Constantinople fell to the Ottoman Empire, the Greek Medieval Empire was the most lasting empire in Europe ever, even more than the original Roman Empire or the Holy Roman Empire (which lasted from year 962 to 1806).
The four B’s at BBBB stand for the Byzantine Imperial motto, “Basileus Basileon, Basileuon Basileuonton”, which in Greek means “King of Kings, ruling over Kingdoms”.
Serbians, who for their most part of the Middle Ages were part of the Byzantine Empire, have a similar acronym in their national shield, CCCC. In the Serbian case, the four C’s stand for “Samo Sloga Srbina Spasava” (“Only Unity Saves the Serbs”). As in the Greek case, every word of the phrase begins with a “S” letter, which in Cyrillic characters is written as a “C” (source).