From reading it on Wikipedia it seems very insignificant compared to Overlord and from what I can tell it captured a small area of land and some German and Italian troops. Did this impact the war in any way?
Key successes of Dragoon:
It opened up the Port of Marseille to allied logistics. These ports used roads and railways that were different from the crowded transportation network of northern France. Eventually about 1/3 of the supplies needed for the final push into Germany came from ports captured during Dragoon.
Dragoon guarded the right flank of the Allied pursuit from Normandy to the Rhine and allowed more risk taking by Patton's forces.
In it's own right, Dragoon increased the casualties suffered by the German Army in pursuit operations. (The Germans decided to retreat out of France after losing in Normandy right as the Dragoon landing began.)
It allowed additional allied forces to deploy into France where they could maneuver, and be supplied, rather than be stuck in the narrow Normandy and Italian fronts.
It had political benefits in that it helped the Allied relationship with the French, supported French resistance forces, increased the prestige of the Allied French armies, and prevented a government not affiliated with Free-French leadership from emerging in southern France after the German withdrawal.
Source: US Army official history Riviera to the Rhine http://www.history.army.mil/html/books/007/7-10-1/index.html
Edit: I should also add that the casualties suffered during the campaign were light compared to German forces, and the investment of naval and logistical resources was probably more productive than they would have been had they been allocated to Normandy or Italy.