Round-off error occurs when a number is approximated to a nearby value due to limitations in representing it precisely in a computer or calculator. This often happens with decimal numbers, where the exact value cannot be stored, leading to a small difference between the actual number and its rounded version. These errors can accumulate in calculations, especially in long computations or iterative processes, affecting the final result. Understanding round-off error is crucial in fields like computer science, engineering, and finance, where precision is important for accurate outcomes and decision-making.