Greece tops the list as the most unique of all countries. Although not technically Cyrillic, it is considered the birthplace of this alphabet. The script is derived from the Greeks, who used the uncial script letters, which are augmentations by consonants and some ligatures from older alphabets. Ancient and middle Greek was recognized as being ostentatious, only spoken by the elite or for matters of government. Notably, citizens of the Roman Empire who had any means of wealth would be encouraged to learn Greek from their tutors, as it would be an embarrassing revelation for attendees of patrician parties. The famous line uttered by Caesar when he was stabbed by Brutus was actually said in Greek, and not a popular story in Latin.
Greece also opened up the world to the teachings of the past, once civilizations had subsided from their conflagration and pillaging. Learning Greek was essential to reading the scripts to understand philosophy, astronomy, mathematics, critical thinking, and the democratic systems of society.
Russia can be considered the largest Cyrillic-using country in the world. Russia is also the largest country by land mass in the world, coming from extremely humble beginnings. The "Rus" people actually started in the city of Kyiv, which was eventually named Kievan Rus. Prince Oleg was named the ruler of this city, which had origins in its Viking natives. The Rus were actually exiles and explorers from the Scandinavian countries, which is why many Norse and Russian people share similar backgrounds, features, and history. The Viking written text was not very practiced, as Viking tales were solidified in history through song, dance, and tales of bravery - which would then be verbally acted out or told to the next generation.
As the Russian empire grew after the strengthening of Moscow, the Kremlin, and the Moscow river, Muscovites needed a language to inscribe their laws and society. They had adopted Cyrillic, which was created in Bulgaria as a derivation of the letters that comprise the Greek alphabet. To this day, those educated in Cyrillic script are able to decipher the Greek alphabet without great difficulty, even without prior knowledge of the language.
If Greece was considered the inspiration, Bulgaria could be considered the one who put it together. The script itself started in Bulgaria during the First Bulgarian Empire. Scores of Bulgarian writers and scholars would get together in the kingdom's best school to devise an alphabet that could be easily used by those who are educated to communicate with one another. This was further solidified during the rise of the Byzantine Empire, which used the school as a Centre for translation into other dialects. The "early Cyrillic" would grow into the script Bulgarians know today.
Cyrillic was created out of the need for the educated Byzantine population to be able to communicate with its Slavic partners. Byzantium was a derivation of the Roman Empire, which spoke both Latin and Greek. As Greek was more common in the region, creating this language proved to be useful to unite cultures.