Cesàro summation is a mathematical technique used to assign a value to certain divergent series, which do not converge in the traditional sense. It works by averaging the partial sums of a series, allowing for a broader understanding of its behavior. For example, if you have a series that keeps growing without bound, Cesàro summation can help find a meaningful value by considering the average of its sums over time. This method is particularly useful in areas like analysis and number theory, where understanding the limits of series is essential.