In terms of liturgical expression, Church Slavonic is to the Eastern Slavs as Latin was to Western Europe - it serves as the official language of the Church and for the Liturgy - and for the longest time, the Bible only existed in Slavonic, but in the 19th century, the Bible was eventually translated into Russian by the Church, so those who were poor could be able to read the Bible on their own - as not everyone could learn Slavonic. Even then, this was obviously a very controversial decision at the time for the more conservative clergy.
It parallels the experience of having the Bible only in Latin in Western Europe for the longest time, but eventually - I think by force of the Protestant Reformation - the Bible began to be translated into different languages, and the Roman Catholic Church began producing versions of the Bible in native tongues. So, we had the Douay Rheims Bible and the Knox to read, but still - the Roman Catholic Church up until Vatican II used Latin. Likewise in Russia, there exists Russian translations, but the official language of the Church is still Church Slavonic.
So yeah, the clerics and the monastics - and the laypeople who know it - in Russia and other Eastern European countries will liturgically read the Bible in Church Slavonic, but for those who want easy access and to be able to read it in their own native tongue, it's an option.
There exists a few versions of the Bible in Russian - the most popular one, the Russian Synodal Version, is published by the scholarship of the Russian Orthodox Church and is the one most in circulation, and used by Orthodox, Catholics, and Protestants in Russia. There also exists the New Russian Translation (the NIV of Russian - translated by Protestants who want to "make the Bible more informal and contemporary" and to "apply a meaning-based translation approach to the Bible"). These two versions are the most common I could find, and I'll probably buy the former if I buy one.
Interestingly enough, the Russian Synodal version was translated from the original Hebrew in the Old Testament and the Greek (which is interesting, because the Hebrew Old Testament is more foreign to Christian Tradition compared to the Septuagint) - and more interestingly, because of how the Russian language has changed, much like the King James version uses older grammar and has impacted the English language, there are some historical linguistic usages that have impacted the contemporary Russian language.
