Pope Francis...prayed for “full unity” with the Coptic Orthodox Church as he received Patriarch of Alexandria Tawadros II for an historic visit in the latest sign of closer ties between the Catholic and Orthodox (sic) worlds.
“We long for the day when, in fulfilment of the Lord’s desire, we will be able to communicate from the one chalice,” he said, acknowledging that there had been “centuries of mutual distrust” between their two Christian churches.
This was the first such meeting in 40 years.
To understand the division between the Coptic Church and Roman Catholicism, one has to look to the split between the Oriental Orthodox churches--of which the Coptic Church is one--and the dominant churches of the West and East, which occured as a result of the Council of Chalcedon in A.D. 451, the Fourth Ecumenical Council, due to what the modern mind almost certainly sees as a technicality.
Chalcedon confirmed that Jesus Christ's humanity and divinity are exemplified as two natures in one hypostasis. More specifically, that Christ is one prosopon (πρόσωπον, often translated into English as "person" though perhaps "identity" could be used) with two natures, fully God and fully man, that are not mixed but in a single and perfect hypóstasis (ὑπόστασις, also often translated into English as "person" though "substance" or "subsistence" could be used).
However, some at the council refused to accept the majority ruling. These non-Chalcedonian Christians insisted on a different Christology: that Christ's natures were not two per se but one, albeit a hybrid, a divine-human nature. Among them were many of the leaders of Egyptian Christians.
Of course, politics was involved in the council's decisions, too, as was the case to varying extents with all of the Ecumenical Councils of the ancient Church.
The majority termed the dissenters Monophysites (monophysite meaning "one nature") and deemed their views dangerously close to Apollanarianism, a heretical Christology that Christ's body was human but His mind was divine, or Eutychianism, that Christ's human nature was dominated by His divine nature--His humanity being "dissolved like a drop of honey into the sea" of His divinity.
However, the non-Chalcedonian Christians term their Christology as miaphysite (meaning "one unified nature") and insist that what the council approved is too close to Nestorianism, which was deemed a hersey twenty years before Chalcedon at the First Council of Ephesus, the Third Ecumenical Council. Nestorianism insists that the human and the divine natures of Jesus are completely separate. It also insists that due to that separation the Virgin Mary cannot be deemed the Theotokos ("Bringer forth of God") but rather the Christotokos ("Bringer forth of Christ").
Non-Chalcedonians are better referred to as the Oriental Orthodox or Miaphysite churches; they are sometimes called the "Old Oriental" churches and their Christology "Alexandrian." They include the Coptic Orthodox, Ethiopian Orthodox, Eritrean Orthodox, the Armenian Apostolic Church, the Syriac (or "Jacobite") Orthodox, and various churches of Oriental Orthodoxy in Indian, such as the Malankara Orthodox Syrian Church.
In the linked-to article instead of "Orthodox" used alone as a name, "Coptic" or "Oriental Orthodox" would have been better in my opinion, to avoid confusion with the Eastern Orthodox Church, the dominant church in Easter Europe and the Middle East.
Images: Francis and Tawadros II; a Coptic cross.