The hyper-Poisson model is a useful tool for dealing with count data that has more variation than expected (overdispersion) or less variation than expected (underdispersion). This model allows for flexibility in handling these cases, unlike the traditional Poisson model which assumes equal mean and variance. The researchers in this study described how the hyper-Poisson model can be applied to real-world data with overdispersion or underdispersion, providing a more accurate representation of the data.