The performance of recommendation algorithms is closely tied to key characteristics of the data sets they use, such as sparsity, popularity bias, and preference distributions. In this paper, we conduct a comprehensive explanatory analysis to shed light on the impact of a broad range of data characteristics within the point-of-interest (POI) recommendation domain. To accomplish this, we extend prior methodologies used to characterize traditional recommendation problems by introducing new explanatory variables specifically relevant to POI recommendation. We subdivide a POI recommendation data set on New York City into domain-driven subsamples to measure the effect of varying these characteristics on different state-of-the-art POI recommendation algorithms in terms of accuracy, novelty, and item exposure. Our findings, obtained through the application of an explanatory framework employing multiple-regression models, reveal that the relevant independent variables encompass all categories of data characteristics and account for as much as $R^2 = $ 85-90\% of the accuracy and item exposure achieved by the algorithms. Our study reaffirms the pivotal role of prominent data characteristics, such as density, popularity bias, and the distribution of check-ins in POI recommendation. Additionally, we unveil novel factors, such as the proximity of user activity to the city center and the duration of user activity. In summary, our work reveals why certain POI recommendation algorithms excel in specific recommendation problems and, conversely, offers practical insights into which data characteristics should be modified (or explicitly recognized) to achieve better performance.