A member of the Coptic church; Also known as the Coptic Orthodox Church of Alexandria. However, that would make the relationship between copticism and Eastern Orthodoxy backwards; The Coptic church is much older than the orthodox, and had no small influence on the early Orthodox church.
This sect derives its name from their Traditional liturgical language, Coptic. The Coptic language is a direct descendant of Ancient Egyptian. However, the majority of Coptic Churches now perform services in the local language.
The church claims its roots in St. Mark's mission to Egypt, about a decade after the events of the gospels. The copts have the luxury of their church being pre-ordained in the old testament: Isaiah 19:19: 'in that day, there will be an altar to the Lord in the midst of Egypt, and a pillar to the Lord at its border.' (anyone here familiar with pillars at the borders of Egypt?) The Coptic church also invented the concepts of monasticism and Catechetical schools, the oldest of which still stands and is used; The Catechetical school of Alexandria.
The Copts are led by a pope, but not the one in Rome: in early christian history, there were 4 centers of Christianity: Rome, Constantinople, Antioch, and Alexandria, each of which had a pope. The Roman pope started to amass power, and eventually got rid of the popes of Constantinople and Antioch, and excommunicated their remaining leaders (Which caused the schism that created the Roman Catholic church and the Eastern orthodox church.
The pope at Alexandria simply Ignored the roman pope, so that now, there are two popes. The current Pope of Alexandria, and of the Coptic church, is Shenouda III.
There is a frequent misconception that the Copts are monophysitic; Monophysitism being the (heretical) belief that Jesus had only one 1 nature, the divine, where most churches belive that Jesus was both mortal and divine. The Coptic Church believed this, as well, but did not sufficiently convince its peers that it believed so at the Council of Chalcedon. This effectively isolated the Copts: Islam was on the rise in Egypt, and, believed to be heretics, few other christian sects would communicate with them.
Currently, there are approximately 10 million Copts worldwide, 9 million of which are in Egypt.