At a basic level, Verdun was intended to bleed France's armies. Falkenhayn, the commanding German officer, hoped to capture a number of French positions, forcing the French to counter attack to retake them, leaving them open to bombardment from German artillery positions. Falkenhayn hoped to recreate the devastation wrought on the French forces that the German artillery had inflicted during a series of battles in the Champagne region the year before.

The initial stages of the battle went well, German artillery saturated the forward lines and French positions were overrun. The greatest of Verdun's defensive fortresses, Douaumont, was captured by a single German sergeant who bluffed the few defenders into surrendering. The French defenders in the region panicked when news of this spread and it seemed as though a retreat was imminent. However, a French officer named Phillipe Petain was given command of the situation and swiftly turned things around. Coordinating the artillery, Petain brought heavy shelling down on the attacking German forces, doing exactly what Falkenhayn had planned to do to the French. Petain also organised a continuous line of supply to keep his artillery well stocked with shells and ammunition for his infantry. What eventuated was a series of attacks and counter-attacks that ultimately resulted in very little being achieved but at the cost of hundreds of thousands of lives. The offensive began in February, 1916 and by May, more then 200,000 German and French soldiers had become casualties. This casualty rate was particularly troubling for the Germans. While the French rotated their units out of the lines and replaced them with fresh ones, the German units were kept in the line and suffered continuously. The continued back and forth continued until December of 1916 when hostilities in the sector finally subsided thanks in part to the Battle of the Somme which required Germany to divert forces to repelling the British offensive. That said, by the end of the German offensive the French had only a single fresh brigade in reserve so had the hostilities continued, who knows what would have happened.

As to why the battle was such a significant event, I would argue that it is because it was so damned horrific. Even by WW1 standards, the horror that the men faced at Verdun was extreme. Flamethrowers were used for the first time as was phosgene gas, the artillery barrages were continuous and absolutely massive and the casualty rates are among the worst suffered. It also became a symbol of French resistance. The French armies had largely been humiliated and on the backfoot until Verdun and their victories there, no matter how small or costly, symbolised their devotion to resisting German aggression. Verdun did do enormous damage to the French forces. It saw the real beginnings of discontent in the French armies which would eventually lead to outright mutiny in some areas.

Source:

1914-1918: The History of the First World War by David Stevenson

The First World War by John Keegan