The name comes from the ancient Greek words (εὐφημία) [eufimia], meaning - "piety, decency; woman who has good (Ev) reputation (φήμη) [fimi] - ".
St Euphemia was killed in the town of Chalcedon during the persecutions of the Emperor Diocletian in 304. A few years later, in 313, the Emperor Constantine declared a policy of religious toleration, and Christians were free to worship again, and so the Christians of Chalcedon built a church over the tomb of the martyr Euphemia.
Nearly 150 years later an important church Council was held in the church where St Euphemia’s tomb was, in 451. An Archimandrite in Constantinople, just over the Bosphorus from Chalcedon, by the name of Eutyches, taught that our Lord Jesus Christ was not both God and man, having a divine and a human nature, but that he was only of two natures before the incarnation, but afterwards he had a single divine-human nature. This teaching was known as “monophysitism” (one-naturedness), but many said it was wrong, and so the Fourth Ecumenical Council was held at Chalcedon to decide the issue. The arguments went back and forth, with neither side giving way, and eventually the bishops at the council decided to ask St Euphemia for her view. She had died for Christ, so which Christ had she died for - the God-man, or the monophysite man become god. Each party wrote its statement of faith, and sealed it and placed it in St Euphemia’s tomb, and the tomb was sealed and guarded for three days while the bishops attending the council fasted and prayed. At the end of the three days the tomb was opened, and the statement of faith that said Christ was of two natures was found in her hand, while the monophyside statement was found at her feet. This was taken to mean that she accepted the first and trampled upon the second. The Council of Chalcedon adopted a definition that said that Christ was of two natures, though some still did not accept it, including Dioscuros, the Patriarch of Alexandria, and eventually the dispute split the Alexandrian Church.
On a superficial level, this story may seem a bit like Paul the Octopus, but a football match is here today and gone tomorrow. The winners rejoice and the losers are sad for a while, but they will go on to play other matches and the result moves into the statistics books. St Euphemia’s choice, however, affected the teaching of the church for all the following centuries.
I don’t want to go into the details of the Definition of Chalcedon (you can read about that here) but rather to see what this story about St Euphemia tells us about the Orthodox Church. There is a sense in which the church is democratic. Bishops met in councils, and they represented their churches, and they voted. But councils of bishops were not necessarily accepted as reflecting the mind of the Church, guided by the Holy Spirit. Some councils were rejected by the Church as a whole.