Question

Why did Germany declare war on Russia

Answer 1

Russia mobilized along the German border. Russia's mobilization amounted to a declaration of war. On August 1, German government declare war on Russia

Answer 2

Your question is in reference to the beginnings of World War I.  The answer is:

Germany felt threatened because Russia mobilized its forces on Germany's eastern borders.

Explanation/context:

The systems of alliances and military plans which were put in place before World War I presupposed a major war between the countries which were tied together with alliances.  The Triple Entente had Britain, France and Russia as allies.  Germany was part of a group of allies in opposition to the Triple Entente.  

So here's what happened to start the Great War (World War I).  When an Austrian prince and his wife were assassinated in Serbia, the Austrian Empire threatened the nation of Serbia with retaliatory action (even though the assassination was carried out by a terrorist group, not the Serbian government). Russia responded to Austria's threat, because Russia was bound to protect its Slavic ally, Serbia. Germany responded to the mobilization of Russian troops, and when Germany declared war on Russia in 1914, they implemented the Schlieffen Plan (drawn up by one of their generals), which called for them to go on attack vs. France.  That pulled France and Britain into the war immediately as well, and the war spread and became a global conflict.