잠이 쏟아지다 literally means "sleep pours" it means "become so drowsy, feel terribly sleepy" e.g. 감기약을 먹었더니 잠이 쏟아졌다 I became so drowsy after taking some cold medication. 그는 오후만 되면 식곤증 때문에 잠이 쏟아졌다 He felt terribly sleepy every afternoon due to languor after meals.