Koine Greek (Ελληνιστική Κοινή, Biblical Greek, New Testament Greek, "common Greek", or ἡ κοινὴ διάλεκτος, "the common dialect") is the form of Greek commonly spoken in Palestine and even Rome in the 1st century A.D., and centuries before and after.
Most of the earliest manuscripts of the New Testament are in Koine Greek. Notable exceptions in the New Testament include the Gospel of Luke, the Epistle to the Hebrews and several of the letters of Paul, which were written in more sophisticated Greek.
Koine Greek was used in the Septuagint, the Greek translation of the Old Testament.
It is a common misconception that modern Greek is the same language that was spoken two thousand years ago - this is not the case - modern Greek and Koine Greek have many differences.