Long run average cost curve is 'U' shaped in the long run due to internal economies and diseconomies of scale.You see when a firm increases in size and  scale of production,it gets several advantages or benefits like it can afford bulk buying of raw materials, can save on transportation cost etc.This reduces the average cost of production of the firm and the curve becomes downward sloping.

However,as the firm becomes exceptionally big,it starts taking several diseconomies or disadvantages like it may not be producing as much as its capacity is.(so the burden of fixed cost has to be born by the firm.)This increases the average cost of production and the curve becomes upward sloping.

Sorry,couldn't have uploaded a diagram.Hope it helps you. :)