This is the 8754th most frequent Russian word.
пищевая
"Пищевая" means "related to food" or "nutritional."
In this sentence, "пищевая" is used as an adjective describing "промышленность", indicating the industry related to food.
Пищевая промышленность играет важную роль в экономике страны.
The food industry plays an important role in the country's economy.
Here, "пищевой" is an adjective describing "краситель", referring to coloring agents safe and intended for use in food.
Она купила пищевой краситель, чтобы украсить торт.
She bought food coloring to decorate the cake.
In this example, "пищевая" modifies "пленка", signifying wrapping material specifically designed for contact with food.