Integer overflow occurs when a calculation exceeds the maximum limit that can be stored in a variable of a specific data type. For example, in many programming languages, an 8-bit integer can hold values from -128 to 127. If you try to add 1 to 127, it wraps around to -128, leading to unexpected results. This issue can cause software bugs and vulnerabilities, especially in critical systems like financial applications or game development. Developers must implement checks to prevent integer overflow, ensuring that calculations remain within the allowable range and maintaining the integrity of the program.