All of the writings of the NT were originally written in Greek. In the 330s
BCE, Alexander the Great conquered most of the Mediterranean. Alexander was a
Macedonian, and, by this time, Macedonia was culturally Greek. When he died,
his kingdom was divided among his generals, who were called the
diadochi.
They were Greeks as well. Because Greek was the official language of
Alexander's administration, it became the
lingua Franca for much
of the Mediterranean. Even in Italy, where Latin was the primary language,
Greek came to exert stronger and stronger influence. Roman schoolchildren had
to learn Greek in school, whereas students in Greek schools didn't have to
learn Latin. The predominance of Greek was very helpful for someone like
Paul, who could write in Greek to churches in
Corinth, Philippi, Thessalonica, and Rome. Wherever Paul went, for the most
part, he could speak Greek. Had he actually made it to Spain, however, his
Greek wouldn't have been as useful.
It only makes sense, then, that when Christians started writing down their
accounts of Jesus' life, or when they started recording his sayings or writing
letters to one another, that they would write in Greek. The kind of Greek that
we find in the NT is called
Koine. It was the kind of Greek that most
people used in letters, conversations, etc.