The Z-Transform is a mathematical tool used in signal processing and control theory to analyze discrete-time signals. It converts a sequence of numbers (like samples of a signal) into a complex frequency domain representation. This transformation helps engineers and scientists understand the behavior of systems, making it easier to design filters and controllers. By using the Z-Transform, one can manipulate and solve difference equations, similar to how the Laplace Transform is used for continuous signals. It provides insights into stability and frequency response, which are crucial for designing effective systems in various applications, including telecommunications and digital signal processing.