XGBoost: predictive, descriptive (or both) model?
You're right that it is a predictive model, but analysing feature importance, partial dependence and other metrics/plots are intended to allow you to gain an understanding of the classification process of models which are often very black-box in nature.

Yes, you can use this to gain some understanding of the underlying data, but I'd be more inclined to say that the primary reason for looking at feature importance is to understand your model rather than to understand your data.