Group Greek
Geography & History After the Macedonian conquest of Greece the ancient political system of polises appeared impossible to conserve. Cultural ties between towns and cities of Greece were strengthening, and a necessity arised to work out a unified form of the Greek language instead of numerous local dialects. This is why after Alexander's death Hellenistic powers of Europe, Asia and North Africa develop a new form of the language called Koiné ("common"). The Greek translation of the Bible was made in this language, it was officially spoken in the Byzantine Empire; the New Greek tongue of modern Greece is a descendant of Koine as well.
Phonetics Koine had some characteristics which reflect another large step in the progress of Greek as a whole. The vowels gradually lose their opposition between long and short ones. Diphthongs are also simplified, and therefore the system of vowels becomes quite simple, unlike the Ancient Greek one. The initial aspiration (which in Ancient Greek was the result of Indo-European *w-, *y-, *s-) also disappears. Consonats change greatly: dz becomes z, aspirated consonants turn to affricates: ph > f, kh > ch [h], th > þ (English unvoiced [th]). A new sound ts appeared. 
Nominal Morphology The morphology also suffers significant changes in this period. The so-called second Attic declension falls out of use, so the noun leós becomes laos; the 2nd declension loses all its feminine nouns as parthenos (a girl) which is later pronounced as parthena, turning to the 1st declension. The vocative case coincides with nominative (the same as in almost all Indo-European groups), and the dual number coincides with plural, also a common process. Moreover, the dative case gradually disappeares. In general, many synthetic traits of such an ancient Indo-European as was Greek, are replaced with analytical forms in Koine. For instance, the suppletive comparative forms and all synthetic comparatives disappear here.
Verbal Morphology The system of the verb goes through the process of analytization. Complex tense forms were developed, e.g. the perfect, the pluperfect tenses are no no longer formed with the help of inflections but with the auxiliary verbs. 
Lexicon About 90% of the vocabulary of Koine continues the Ancient Greek forms. Along twith that, new lexicon is acquired from Latin, Romance, Slavic (after the 6th century) and Turkish (from the 13th century) languages.
Writing Greek alphabet
Close Contacts Actually Koine inherited quite a lot from the Attic and Ionic dialects of Ancient Greek. In the Byzantine period, Koine enters the so-called Balkan language unity, sharing common features of morphology and syntax with the languages of the Balkan peninsula: Albanian, Romanian, South Slavic, and even Turkish.
Sample Γραμματα εστιν εικοσιτεσσαρα απο του α μεχρι του ω. γραμματα δε λεγεται δια το γραμμαις και ξυσμαις τυπουσθαι  γραψαι γαρ το ξυσαι παρα τοις παλαιοις 'ως και παρ' 'Oμηρω "Nυν δε μ' επιγραψας ταρσον ποδος ευχεαι α'υτως". 

(Dionysii Thracis. Ars Grammatica. 1st cent. BC)

Picture Byzantine Painting
More info