The U-shaped long-run average cost curve represents the relationship between the average cost per unit of production and the level of output in the long run. This curve typically illustrates economies of scale at lower levels of output, where increasing production leads to a decrease in average costs, followed by diseconomies of scale at higher levels of output, where average costs begin to rise as production increases further. This shape highlights the efficiency of firms as they expand production and the eventual challenges they face as they grow too large.