Vladimir Moss offers an interesting perspective on how he, being a Russian Orthodox Christian, understands the shroud:
A recent book on the Turin Shroud, the most detailed and comprehensive yet[Ian Wilson, The Shroud: the 2000-Year-Old Mystery Solved], raises again the question: how should we, as Orthodox Christians, evaluate and react to this extraordinary object? In the 1970s the ROCOR [*] Deacon (now OCA “Archbishop”) Lev Puhalo wrote several articles against it, labelling it a medieval forgery. And in this judgement he has been followed by many people, including many scientists. However, nobody has yet been able to give us even a remotely plausible answer to the question: if it is a forgery, how was it made? And until somebody answers this question, the central question: is it the authentic burial shroud of Christ? must remain open…
This is not simply a scientific matter. For many, including the present writer, the most powerful argument for the Shroud’s authenticity is its quite extraordinary beauty, a beauty of an altogether higher nature than that of any merely human artefact. Now many may retort: beauty is in the eye of the beholder, its perception is a purely subjective matter. But this is not true. When the envoys of St. Vladimir came back to Kiev from Constantinople, recommending that their prince adopt the Orthodox Faith on account of the extraordinary beauty of the services, they were not being frivolous or naive.
Beauty – transcendent, spiritual beauty – is an argument, and a powerful one. For we all instinctively understand that truth must be beautiful, otherwise it is not truth. The foremost book of Orthodox spirituality, the Philokalia, means “the love of beauty”. True beauty is precisely a vision of truth, of the reality of things in and through created matter. God is discerned in the beauty of holiness.
[ . . . ]
“That is all very well”, says the sceptic, “but the Shroud is a ‘holy’ object owned, not by the Orthodox Church but by the Pope, of which there is no record in the Orthodox East, and which has been proven by carbon-14 to have been created in the fourteenth century. The onus is on you to prove that it is in fact Orthodox in provenance and dates to the first century. . . .
* Who or what is ROCOR? According to Wikipedia:
The Russian Orthodox Church Outside Russia (Russian: Ру́сская Правосла́вная Це́рковь Заграни́цей, Russkaya Pravoslavnaya Tserkov’ Zagranitsey), also called the Russian Orthodox Church Abroad, ROCA, or ROCOR, is a semi-autonomous part of the Russian Orthodox Church.
ROCOR was formed as a jurisdiction of Eastern Orthodoxy as a response against the policy of Bolsheviks with respect to religion in the Soviet Union soon after the Russian Revolution of 1917, and separated from the Russian Church of the Moscow Patriarchate in 1927 after an imprisoned metropolitan Sergius (Stragorodsky) pledged the Church’s qualified loyalty to the Bolshevik state. The Russian Orthodox Church Outside of Russia officially signed the Act of Canonical Communion with the Moscow Patriarchate on May 17, 2007, restoring the canonical link between the churches. Critics of the reunification argue that the issue of KGB infiltration of the Moscow Patriarchate church hierarchy has not been addressed by the Russian Orthodox Church.
The Church has around 400 parishes worldwide, and an estimated membership of over 400,000 people. Of those, 138 parishes and 10 monasteries are in the United States, with 27,700 adherents and 9,000 regular church attendees. Within the ROCOR there are 13 hierarchs, and also monasteries and nunneries in the United States, Canada, Australia, New Zealand, Western Europe and South America.
Picture is a chapel at ROCOR’s headquarters (from Wikipedia)