Long-run marginal cost refers to the additional cost incurred by a firm when it produces one more unit of output in the long run, when all inputs can be varied. This concept is crucial for understanding how firms decide on the optimal level of production to maximize profits, especially in a competitive market where firms are price takers. It plays a significant role in shaping the supply curve of a competitive firm, illustrating how costs influence production decisions over time as firms adjust their capacities and inputs.