Mobile data traffic is characterized by complex spatiotemporal fluctuations that are linked in entangled ways to the mobility and diverse activities of the mobile network subscribers. Unraveling such dynamics and understanding their root causes are challenging tasks that call for dedicated, complex data analysis tools. In this paper, we propose to employ Exploratory Factor Analysis (EFA) as a unified approach to identify both spatial and temporal structures hidden in the mobile data traffic. We provide a brief introduction to the EFA methodology, discuss how it can be tailored to a networking context, and outline its advantages in terms of versatility, unsupervised nature and interpretability of results. Experiments with large-scale measurement data collected in two urban regions demonstrate the effectiveness of the approach, which allows recognizing and explaining a variety of fundamental structures that underpin real-world spatiotemporal traffic dynamics. A thorough discussion of the results provides interesting insights, including that a reasonably small number of latent factors can describe well the majority of temporal and spatial structures observed in mobile traffic demands, providing valuable insights into key spatiotemporal patterns of population and becoming a valuable asset in understanding the attractiveness factors in urban areas.