Discontinuities refer to points in a function where it is not continuous. This can occur for various reasons, such as a sudden jump in values or an undefined point. Understanding discontinuities is crucial in calculus, as they can affect the behavior of functions and their graphs. Common types include removable, jump, and infinite discontinuities, each with distinct characteristics. In practical terms, discontinuities can represent real-world phenomena, such as sudden changes in temperature or stock prices. Identifying these points helps in analyzing trends and making predictions. Thus, recognizing discontinuities is essential for both theoretical and applied mathematics.