The D-Day invasion of France by the Allies was important because it was a major step towards defeating Germany. By invading France, the Allies were able to actually destroy the Nazi regime rather than having to make some sort of peace with that regime.
Without this invasion, it would have been very hard for the Allies to destroy Hitler's regime. The Russian push from the East and the American invasion of Italy simply did not put enough pressure on Germany and would not have caused Germany to surrender unconditionally. By successfully invading France, the Allies ensured that Germany would lose the war and be forced to surrender unconditionally.
D-Day, June 6, 1944, is the day that British, Canadian, American and Free French Allied Forces invaded occupied France, and began the liberation of Europe from Nazi Germany.
D-Day was not the turning point in the war; the tide had clearly turned in the Allies' favor the previous year, as the Soviet Red Army was progressively moving the Eastern Front westward. However, the Soviets' progress was slow. D-Day helped to dramatically accelerate the German defeat by opening up a front in the West, so that they could not devote all of their resources to fighting the USSR. With the Allies now battling the Nazis on both sides, the war was concluded in Europe within a year.
Some argue as well that D-Day prevented a Soviet domination of all of Europe (instead of just the East), as well. Had the Americans/British not put their armies on Western European soil, the Soviets might well have been tempted to occupy the entire continent at the war's end.
If they had spent couple more years 'building up' their forces miles away from the main (Eastern) war front, then the war would have ended with the victory of the Soviet Union and without much Anglo-American involvement.
'D-Day' is more of a political event - it actually prevented USSR from capturing territory east of the Elbe.