Transfer functions are a mathematical representation of the relationship between input and output in a system, typically in the context of control systems or signal processing. They are commonly used to model the dynamics of linear time-invariant systems and can be expressed as a ratio of polynomials in the Laplace domain. Transfer functions allow engineers to analyze and design systems by studying their frequency response, stability, and transient response. They are a fundamental tool in the field of control theory and are essential for understanding and predicting the behavior of dynamic systems.