In this context, Galicia does not mean the region in northwestern Spain.
Once Austria-Hungary declared war on Serbia, the Russians mobilized their armies against Austria-Hungary in compliance with their alliance with Serbia. The Austrians knew that they needed to strike quickly as the Russian army was much larger, so Austria needed the advantages of time and surprise if they would stand a chance against the Russians. Thus, Austria launched its attack on Russian Poland, hoping to gain the upper hand and be on the offensive against the Russians. The Austrians were also hoping that they would receive support from Germany, unaware that the Russians had executed an invasion of East Prussia that would keep German forces in the east occupied.
For Austria, the results were disastrous. They were outmatched by the Russian army that swept into Austrian territory and took the province of Galicia. A large number of its Slavic forces surrendered to the Russians, offering to fight for Russia against their empire. While both sides had casualties over 200,000, Russia claimed success and penetrated 160 km into Austrian territory. In Prussia, however, Russia suffered a humiliating defeat at Tannenberg due to poor leadership, badly-trained troops and antiquated equipment (including maps that were inaccurate).
Galicia established Austria as the weakest of the major European powers and it was the one area where Russia consistently won in warfare. It established a pattern: initial Russian success against Austria, after which the Germans would launch a counteroffensive that would drive the Russians back into Russian territory. Unlike the war on the Western Front, the war on the Eastern Front was one of movement – battles changed the possession of hundreds of kilometers of land, rather than the meters that changed hands in the west.
One critical significance of the Battle of Galicia is that Germany recognized it would need to provide constant assistance to Austria, and therefore could not concentrate its forces in the west. Germany was by far the strongest of the Central Powers and its resources were strained by its Austrian ally. The longer the war lasted, the more this became a factor, and the more it was likely to affect the outcome of the war.