It goes back to the great schism in Christendom of 1054, between the western chuch centred on Rome and the eastern on Constantinople. (See map)
Croatia, where they speak much the same language as Serbia, but using the Latin script rather than the Cyrillic; and where the principal confession is Roman Catholic rather than Greek Orthodox, was part of the Austro-Hungarian Empire prior to WW1.
Pan-Slavist tendencies link Russia to support of the Orthodox parts of Eastern Europe. The Serbs were also influential in the eviction of the Turks from Europe.
All these factors have created a bond between Russia and Serbia which has lasted for centuries.
This is the short answer!