The creeping barrage changed all that. Concentrated, accurate artillery fire, en masse, was used to create a "screen" in front of the infantry. Not only would these barrages cut barbed wire and other obstacles, but they dramatically reduced the amount of enemy fire that could reach the infantry as the intensity of the barrage was so high that enemy fire simply couldn't get through it.
As the infantry advanced the barrage would "lift", moving ahead of the infantry. As the infantry were nearing the enemy trenches, the enemy would be receiving this murderous barrage, and would be unable to perform defensively. Then, the barrage would lift to behind the enemy front line, in order to prevent counter attacks or secondary trench lines from firing on the allies. This would leave the allied soldiers with a short sprint to reach the enemy trenches, and they could be in them before the Germans had time to return to their guns.
The catch is, an effective creeping barrage relies on precise timing. If the barrage gets too far ahead of the infantry, the German defences can get inside it, and cut down the soldiers. If the barrage gets too far behind, your own men will be hit by it.
The question then, is how do you coordinate a creeping barrage in a time that lacks the kind of sophisticated communication equipment that would allow for accurate real time adjustments? You have to have the entire thing perfectly timed out from the outset. To the second. And to make that work, the infantry have to maintain a slow, careful pace. So they walked.