The Old Believers are a group within the Eastern Orthodox Church, primarily the Russian Orthodox Church, who continued to follow the old rituals and litigation of the Church from before the reforms of Nikon of Moscow in in 1650s and 1660s.
The actual reforms that took place were, to modern day historians looking back, incredibly trivial – they were simply things like changing a walking procession from walking clockwise to walking anticlockwise, or changing the way you hold your fingers when making the sign of the cross. However, in the time period religion and rituals were incredibly important and many people centred their lives around them, meaning that any slight changes and the suggestion that you were worshipping wrong would have truly terrified many people. There was also the fact that, according to the dissenters, Nikon did not adequately consult the other members of the ROC or form any sort of council before undertaking these reforms.
The consequence of this division, however, was fairly major. The state church, as of 1666, publicly denounced and shunned those who wished to remain loyal to the old traditions to such an extent that the Old Believers then officially lacked all civil rights. In fact, the state actually had the most active Old Believers arrested. from 1685 onwards, there began a great prosecution of Old Believers which included torture and execution, and many of them fled the country all together, heading for places like Lithuania where there is still a community today. Nevertheless, the Old Believers continued to practice and actually became the largest denominations in many rural areas of Russia. Old Believers continued to be oppressed by the states for many decades to follow, often to differing extremes. One example was having to pay twice as much tax (under Peter the Great). Overall the Russian state say the Old Believers as a continuing threat to their control.
In 1721, Catherine the Great passed an act which finally allowed the Old Believers to practice their faith without persecution, and in 1905, when Nicholas II passed an act ending religious persecution in Russia, they gained the ability to build churches and form an organised religion once more.