Greeks and Greek speaking Christians constituted the greater part of the early Christian Church. Although Rome had achieved the political unity of the whole world, it was the Greeks who who had a achieved a cultural unity throughout the Mediterranean world and beyond. It was their language, ideas and outlook that swept a good part of the known world. The first contact of the Greeks with Christ was related in the Gospel of John (Jn 12.20-24). Some Greeks approached Phillip and Andrew and asked to meet with Jesus. They were eager to hear the new ideas espoused by this new teacher.
Greeks have always been travelers; cosmopolitan wanderers, like Homer's Odysseus, searching and restless for new experiences and ideas. Thucydides described the Ancient Greeks as "people who could not rest or permit others to rest."
Jesus realized that these Greeks with "a searching spirit and troubled mind" represented an opportunity to spread his message beyond the boundaries of Israel. The Greeks had established cities throughout Asia Minor, Palestine and Syria and they did not confine themselves there but communicated with the outside world through trade and travel. These cities became centers of Hellenic learning and civilization. Only a segment of Jewish society resisted the Hellenism which most Jews welcomed. Hellenized Jews, spoke and wrote Greek, including some of Christ's disciples. Knowledge of the language was widespread. The Hellenization of the Jews was voluntary, very much like the Americanization of Greeks, Italians and Jews today in the United States. This voluntary self-Hellenization enabled Christianity to transform itself from a Jewish creed into a universal religion.
Greek thought and philosophy also played a very important role in the evolution of Christianity. For example, Plato taught that the visible world reflects an invisible, much greater and better world. His teachings also redefined the whole question, Who is a good man? Evolving from man as an ethical being to man as a spiritual person. Armed with platonic teachings, pre-Christian Greeks sought "pnevmatiki gnosis" or spiritual knowledge leading to a divine exaltation of God's glory and ultimately union with God or "Theosis" Christianity thus inherited the ethical teachings and admonitions of the Bible as well as the spiritual quest of the Ancient Greeks. In so doing it embodied both the ethical and spiritual, addressing those needs in ordinary human beings. Greeks prepared the civilized world to accept the word of Christ and helped sow the seeds of Christianity and transform it into an ecumenical, universal faith for everyone of us.
For a much more detailed discussion of these concepts, I highly recommend reading: Understanding the Greek Orthodox Church by Demetrios Constantelos.