Final answer:
The most significant contribution of the Byzantine Empire was its architectural achievements, particularly in the building of religious structures like the Hagia Sophia and the spread of Christianity throughout the eastern Mediterranean, which have had a long-lasting impact on both historical and contemporary architecture and religious practices.
Step-by-step explanation:
The most important contribution of the Byzantine Empire can be subject to different interpretations, but many would argue that its architectural achievements, particularly in the realm of religious construction, are among its most lasting and influential. The Byzantine Empire is renowned for its development of a distinctive architectural style that served both the new Christian religious order and the empire's administrative purposes. Notable architectural contributions include the innovation of the pendentive dome, which allowed for circular domes to be placed over square rooms, as exemplified by the Hagia Sophia in Constantinople. Moreover, the Empire's role in the spread of Christianity throughout the eastern Mediterranean, translating the Bible into various languages and embracing diverse Christian liturgies, was pivotal in shaping the religious landscape of the region.
Despite engaging in military conquests and some technological innovations, these were not as pivotal in the grand scope of the Byzantine legacy as its contributions to architecture and religion. Furthermore, Byzantine diplomacy and international relations, particularly the establishment of the 'Bureau of Barbarians', showcased the emphasis on strategy and alliances over outright military conquest. The impact of the Byzantine Empire on the development of early Christian and Islamic architecture, as well as its influence on art up to the present day, solidifies its architectural and religious contributions as its most significant achievements to the world.