A monotonic function is a type of function that consistently increases or decreases without any interruptions. If a function is monotonic increasing, it means that as the input values increase, the output values also increase. Conversely, a monotonic decreasing function means that as the input values increase, the output values decrease. Monotonic functions are important in mathematics because they help in understanding the behavior of functions over specific intervals. They can be useful in various fields, including economics, physics, and statistics, where predicting trends and behaviors is essential.