The connection between these two is that World War I served as a catalyst for the Russian Revolution. Russians had been very unhappy with their government for decades, and WWI pushed them over the brink to rebellion.
WWI was a failure for Russia. Its armed forces were defeated badly on the field of battle. At home, things were bad as well. There were huge shortages of food and people were starving. The tsar tried to suppress the protests of the people who were hungry and the soldiers who were sick of the war, but he had lost a lot of his prestige as his army (which he was actually leading by the end of the war) did so poorly in battle.
Faced with disasters both in the military and economic realms, Tsar Nicholas gave in and abdicated his throne. In this way, the Russian Revolution was set off by failures connected to WWI.
A first Russian revolution in 1905 that stemmed from labor unrest, student unrest, agricultural problems and discrimination against ethnic groups led to a series of reforms, such as the creation of the Duma or lower congress and a 1906 constitution. However, little more than a decade later, the government's mismanagement of World War I pushed the country directly over the brink into full scale communist revolution. First, because Russia was technologically behind its German enemy, it suffered its highest war casualties ever (and this in a country that had endured a Napoleonic invasion). Second, corruption was rampant and Tsar Nicholas II repeatedly dissolved the Duma when it wouldn't do as he wanted. People therefore increasingly lost faith in the government's ability to solve problems. Third, the war effort disrupted the economy and, finally, the intellectual class threw its lot in with the disgruntled workers. One can make a strong argument that without the highly destabilizing effects of a disastrous war overlaid on an already unstable situation, Russia might have lurched towards a more modern state without a full-scale revolution. The war, however, led directly to the revolution.