An Overflow Error occurs in computing when a calculation exceeds the maximum limit that a data type can hold. For example, if a program tries to store a number larger than what a byte can represent (which is 255), it will result in an overflow. This can lead to unexpected behavior or crashes in software applications. Overflow errors can happen in various programming languages and environments, affecting both integer and floating-point calculations. Developers often implement checks to prevent these errors, ensuring that calculations remain within safe limits and that the program runs smoothly without interruptions.