This is the 394th most frequent Japanese word.
大きく
"大きく" means "largely" or "in a big way."
Here, '大きく' is used to describe the manner in which the growth occurred (significantly or greatly).
大きく成長した子供たちは、もう小さな手ではありません。
The children who grew significantly are no longer with small hands.
In this case, '大きく' is used to emphasize the extent of the action (thoroughly).
部屋を大きく掃除したので、とてもすっきりしました。
I cleaned the room thoroughly, so it feels very refreshed.
In this sentence, '大きく' indicates the degree to which the change in demand is happening (significantly).