Difference equations are mathematical expressions that relate a function or sequence to its previous values. They are similar to differential equations, but instead of dealing with continuous changes, they focus on discrete changes. This makes them useful in various fields, such as economics, engineering, and computer science, where systems evolve in steps rather than continuously. These equations can be used to model a wide range of phenomena, from population growth to financial investments. By solving difference equations, one can predict future values based on past data, making them a powerful tool for analysis and forecasting in many applications.