The term "order" in thermodynamics refers to the differentiability of a thermodynamic potential during a phase change. A first-order phase transition involves a discontinuity in the first derivative of the potential, such as entropy or volume, while a second-order transition involves continuity in the first derivative but a discontinuity in the second derivative. This classification helps in understanding the nature of phase transitions and their associated thermodynamic properties. The concept is essential for analyzing systems undergoing phase changes under varying physical parameters. Understanding the order of phase transitions is crucial for applications in material science and thermodynamics.