edit: Just to clarify I mean short term significance ie. how it effected the rest of the war?
Some would consider the battle of Stalingrad to be a definitive turning point in the war. A year earlier (1941) the Wehrmacht had been turned back during the battle for Moscow but the situation in Russia was far from certain. The following year (1942), under Hitlers orders, the German military turned its attention south and Army Group South rapidly advanced towards the Caucuses. As the demand for oil was becoming a critical concern for the Wehrmacht at this point in the war it was seen as necessary by Hitler to secure the oil fields within the Caucuses to fuel his military, as well as deny the Soviet Union of its main source for oil production.
Advance of Army Group South in 1942.
In early July as Army Group South pushed towards the Caucasus it was further split into two separate Army Groups, A and B. Army Group A would continue the push towards the Caucuses while Army Group B would secure the northern flank in a push towards the Don River and then ultimately the Volga river.
As Army Group B (The Sixth Army) closed in on the Volga river Soviet forces retreated into the city of Stalingrad. Although it was a major production and transportation hub in the southern part of Russia, capturing the city itself bore little strategic value concerning the campaign at large.
The Sixth Army advanced on the city of Stalingrad in order to destroy the remnants of the Soviet 62nd Army within. From the start of the battle in the suburbs of the city the Sixth Army became bogged down in urban combat. The advantages the Wehrmacht enjoyed over the Soviet Army were greatly reduced within an urban setting. The rapid mobilization of armored formations became a non factor, while armored units themselves such as tanks or assault guns were easily destroyed within a cities confines. The air superiority enjoyed by the Luftwaffe was reduced, especially when Soviet soldiers were ordered to hold their lines as close to the assaulting Germans as possible.
Fighting continuous battles within the city from September through to November the Sixth Army found itself being bled to death by an enemy that refused to capitulate. Reserve forces were continuously taken off of the flanks to replace losses sustained within the city, leaving the flanks north and south of the city increasingly vulnerable. The high command of the Soviet Army would take note of the precarious position of the Sixth Army in the closing months of 1942.
As the situation became less critical in the battles around Moscow Soviet forces were hastily redeployed south to the flanks of Stalingrad. On November 19th the Soviets launched the massive Operation Uranus that attacked into the weakened flanks of the Sixth Army. Three days later the Sixth Army would find itself encircled in Stalingrad within many of its own divisions severely weakened.
As the Sixth Army, or Army Group B had become surrounded the flank of Army Group A that was further south in the Caucus region came under immediate threat. Army Group A would retreat out of the Caucus region before being cut off by Soviet forces. In this regard the entire battle plan of the Wehrmacht for 1942 was turned into a catastrophic failure.
Ultimately the Sixth Army would be virtually destroyed by the time it surrendered in February of 1943. The Sixth Army had accounted for nearly a quarter of the entire German military and such staggering losses could not be replaced, either in men or equipment.
The initiative in the south would definitively swing in favor of the Soviets for the time being. I think it must also be noted that heading into 1943 the Soviet armaments industry was starting to rebound from the its critical state in 1941-1942. The German armaments industry would struggle to match Soviet production from here on out, especially with the Allied bombing campaigns that got underway in 1943.