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In a little more detail, ROCOR stands for Russian Orthodox Church Outside of Russia.

It was established by the Russian bishops outside Russia (many in North America which was canonically an Archdiocese of the Russian Church since our first Orthodox missionaries and bishops were from Russia) under a grant of authority from St. Tikhon, the first Patriarch of Moscow after the restoration of the office abolished by the Westernizing Tsar Peter. After his imprisonment by the Bolsheviks, St. Tikhon issued a ukase directing the bishops outside Russia to govern the Church until normal relations could be reestablished with the Patriarchate.

The fragmenting of Orthodoxy into ethnic 'jurisdictions' in North America, and outside of traditionally Orthodox countries generally, dates to this period: the Ecumenical Patriarchate, in the wake of the loss of the Second Greco-Turkish War, the Rape of Smyrna, and the forced exchange of populations, claimed juridiction over the Americas and established a parallel Greek Orthodox Archdiocese.

ROCOR, of course, gained numbers as Russian Whites went into exile (St. John of Shanghai and San Francisco led a great many Russians first to China, then to the U.S., and there was a diaspora a Russian Whites into Western Europe, esp. France).

In the 1930's the Russian church in North America split over a dispute between the local metropolitan and the ROCOR Holy Synod over the traditional rights of a local metropolitan. Those who followed the metropolitan are now called the OCA, and are regarded by Moscow, Bulgaria and the Church of Japan (though not by any of the ancient patriarchates or other national churches) as an autocephalous church.

It's not clear to me, though, how much of the schismatic wing of ROCOR are actually the children and grandchildren of marytrs and confessors of the Bolshevik yoke, and how much of it is rigorist converts. ROCOR had a great deal of attraction for a certain strain of convert, an a lot of them seem to align themselves with the anti-Moscow hardliners.

Of course, recent actions by the Moscow Patriarchate, most notably the proclaimation of the glorification of Tsar Nicholas and his family as the Royal Passion-Bearers (a specific class of saint who dies in likeness to Christ's Passion neither resisting not removing himself or herself from harm's way because of Christian convictions--in this case the coronation oath as Tsar--but is not killed for refusing to deny the Faith), and the glorification of numerous martyrs whose names and deaths are know from the now-opened KGB archives, have (I think rightly) been taken by the hierarchs of ROCOR as
meeting the conditions of St. Tikhon's ukase that normal relations with the Patriarchate can be reestablished.