The title has been in use since the 3rd century, in the Syriac tradition (as Classical Syriac: ܝܳܠܕܰܬ ܐܰܠܳܗܳܐ, translit. Yoldath Aloho) in the Liturgy of Mari and Addai (3rd century) and the Liturgy of St James (4th century). The Council of Ephesus in AD 431 decreed that Mary is the Theotokos because her son Jesus is both God and man: one divine person with two natures (divine and human) intimately and hypostatically united.
Theotokos is also used as the term for an Eastern icon, or type of icon, of the Mother with Child (in the western tradition typically called a Madonna), as in "the Theotokos of Vladimir" both for the original 12th-century icon and for icons that are copies or imitate its composition.
The title of Mother of God (Greek Μήτηρ (του) Θεοῦ; abbreviated ΜΡ ΘΥ, Latin Mater Dei) (and equivalents) is most often used in English (and other modern western languages), largely due to the lack of a satisfactory equivalent of Greek τόκος / Latin genetrix.
Theotokos is an adjectival compound of two the Greek words Θεός "God" and τόκος "childbirth, parturition; offspring". A close paraphrase would be " whose offspring is God" or " who gave birth to one who was God". The usual English translation is simply "Mother of God"; Latin uses Deipara or Dei Genetrix. The Church Slavonic translation is Bogoroditsa (Russian/Serbian/Bulgarian Богородица). The full title of Mary in Slavic Orthodox tradition is Прест҃а́ѧ влⷣчица на́ша бцⷣа и҆ прⷭ҇нод҃ва мр҃і́а (Russian Пресвятая Владычица наша Богородица и Приснодева Мария), from Greek Ὑπεραγία δεσποινίς ἡμῶν Θεοτόκος καὶ ἀειπαρθένος Μαρία "Our Most Holy Lady Theotokos and Ever-Virgin Mary". German has the translation Gottesgebärerin.