What is meant by the terms ‘canonical’ and ‘non-canonical’?

An excerpt from 'Christian Union? An Orthodox Christian's Guide to Ecumenism: Past, Present and Future'

In the sense that this question uses it, the word ‘canonical’ means ‘official’ or ‘in communion with world Orthodoxy’. Churches that are not in communion with official Orthodoxy are therefore accused by these ‘official’ churches of being ‘non-canonical’. However, the word ‘canonical’ actually means obeying the canons of the Church Councils, so the words ‘canonical’ and ‘ecumenical’ are mutually exclusive. Even Fr. Alexander Schmemman, a famous Orthodox ecumenist, criticized the obsession with associating the word ‘official’ with ‘canonical’:

..it is not the decision of a Patriarch or his synod that creates and guarantees “canonicity”, but, on the contrary, it is the canonicity of the decision that gives it its true authority and power. Truth, and not power, is the criterion, and the canons, not different in this from the dogmas, express the truth of the Church. And just as no power, no authority can transform heresy into orthodoxy and  make white what is black, no power can make canonical a situation which is not canonical.^[1]

It is not power or official recognition that defines Orthodoxy, but the exact keeping of the saving Orthodox faith. St. Mark of Ephesus, in rejecting the false union of the Council of Ferrara-Florence, found himself outside official Orthodoxy as the only Orthodox bishop left at the Council who did not sign the agreement of union between the Greek Orthodox Church and the Papacy. Denounced as a heretic by the Pope, Saint Mark answered:

I express not my opinions, I introduce nothing new into the Church, neither do I defend any errors. I keep the doctrine which the Church, having received from Christ our Saviour, has kept and still keeps. This doctrine was also held to by the Church of Rome, unanimously with the Eastern Church, until the start of the Schism. Even during this present synod, you have praised this exact pious worship of the past. No one can censure or condemn this pious teaching. Therefore if I remain firm in this doctrine, and do not wish to reject it, how is it possible to accuse me of being a heretic? 

Orthodox Christians who wish to remain faithful to traditional Orthodoxy do not need to explain or justify their position because the faith they hold is not a modern innovation, but the Orthodox Faith.

^[1] St. Vladimir’s Theological Quarterly, Vol. 8, No. 2 (1964) pp. 67-84.