Difference equations are mathematical expressions that relate the values of a sequence at different points. They are similar to differential equations, but instead of dealing with continuous functions, they focus on discrete values. These equations are often used to model situations where changes occur at specific intervals, such as population growth or financial investments. In a difference equation, the value of a sequence at a certain point is expressed in terms of its previous values. For example, a simple first-order difference equation might state that the next value is equal to the current value plus a constant. This makes difference equations useful in various fields, including economics, engineering, and computer science.