The celebration of Novy God (Новый год, i.e. New Year) in Russia has a deep cultural, historical and political dimension behind it.
Before the 16th century in Rus’ (ancient Russia) March was considered as the first month of the year (like in ancient Rome). After 7000 AM (Year After Creation, i.e. 1492 AD) the tradition of celebrating New Year in September (like in Byzantium) set in.
On December 20, 7208 AM (Byzantine calendar), Peter the Great issued a decree according to which January 1 was the first day of 1700 AD (Julian calendar). It also contained instructions how to celebrate it (during 7 days): wishing each other prosperity, decorating trees (pine, spruce and juniper), burning bonfires at night, arranging fireworks, etc.
But by 1700 most European countries had adopted the Gregorian calendar, so Russia celebrated New Year’s Day 11 days later than other European countries (which Peter the Great saw as a model for Russian modernization). Russia adopted the Gregorian calendar only in 1918. From 1930 to 1947 New Year’s Day was not celebrated in the USSR (it was seen as a bourgeois relic).
P.S. In Russia on January 13 (at midnight) we celebrate Stary Novy god (старый Новый год, literally: Old New Year), also known as the Orthodox New Year. It is the start of the New Year according to the Julian calendar (and an unofficial holiday).
UPD. С наступающим старым Новым годом! Happy Orthodox New Year!