The title is most usually associated with the shahanshah (shah of shahs, i.e., king of kings, indeed translated from Greek as basileus tōn basileōn, later adopted by the Byzantine emperors) of Persia under the Achaemenid dynasty whose vast empire in Asia lasted for 200 years up to the year 330 BC, which was later adopted by successors of the Achaemenid Empire whose monarchial names were also succeeded by "the great."
Great kings referred to each other as brothers and often established close relationships through marriages and frequent gift exchanges.
[2] The case of the maharaja ("great raja," the great king and prince, in Sanskrit and Hindi) on the Indian subcontinent, initially reserved for the regional hegemon such as the Gupta, is an example of how such a lofty style can get caught in a cycle of devaluation by "title inflation" as ever more, mostly less powerful rulers adopt the style.
Alternatively, a more idiomatic style may develop into an equally prestigious tradition of titles because of the shining example of the original.
Thus, various styles of emperors trace back to the Roman imperator (strictly speaking a republican military honorific) or the family surname Caesar (turned into an imperial title since Diocletian's tetrarchy).