The purpose of mathematical modelling is to discover the underlying factors and drivers of a particular situation, develop tools to map, model and predict their behaviour and impact on one or more outcomes. These are then most commonly use to predict the effect of different actions and test different scenarios, as well as plan future activity and resources.
One recent project saw these techniques applied to daily sales of each service of a multi service organisation. The result was a tool that was able to model the daily demand for each service to within 5% accuracy. Another common application is financial cost modelling.