State functions are properties that depend only on the current state of a system, such as temperature, pressure, and volume. Other state functions include internal energy and potential energy, which can be identified using the principle that differentials of properties are exact. To determine additional state functions, one must understand the conditions and relationships governing these properties. The discussion emphasizes the importance of recognizing the fundamental nature of state functions in thermodynamics. Understanding these concepts is crucial for analyzing thermodynamic systems effectively.