Neither side really won. The British and French, who started the battle, won some ground, but it wasn't much and their casualty rate was very high. The British & French lost about 620,000 men; the Germans lost about 500,000.
The goal of the battle was to make a breakthrough against the German lines and to take some of the pressure off of French troops who were fighting the Germans at Verdun. I believe the casualties were higher at the Battle of the Somme than at Verdun.