。
Rice grows in warm climates.
Literal
Rice [topic-は] warm climate's under [in-で] grows.
成長する is the formal Sino-Japanese verb 'to grow,' often used for organisms, economies, and abstract concepts. 暖かい気候の下で is 'under warm climate conditions' — 下 (read もと here, not した) means 'under/below' in the abstract sense of 'under the influence/conditions of.' A formal-register way to describe ecological conditions.