Grenades were important for clearing out any trenches; a good illustration of this is the fighting on the Somme, esp. on the first day, and in subsequent attacks throughout august. The fighting here was grenade driven, with both sides bombing the other out of dug outs.

In terms of the effect on the war, outside of tactical considerations, not much. Grenades were merely part of the increasing sophistication of infantry methods, which by 1916 were on their way to revolutionizing small unit warfare.