Although popularly used in big-data analytics, dimensionality reduction is a complex, black-box technique whose outcome is difficult to interpret and evaluate. In recent years, a number of quantitative and visual methods have been proposed for analyzing low-dimensional embeddings. On the one hand, quantitative methods associate numeric identifiers to qualitative characteristics of these embeddings; and, on the other hand, visual techniques allow users to interactively explore these embeddings and make decisions. However, in the former case, users do not have control over the analysis, while in the latter case. assessment decisions are entirely dependent on the users perception and expertise. In order to bridge the gap between the two, in this article, we present VisExPreS, a visual interactive toolkit that enables a user-driven assessment of low-dimensional embeddings. VisExPreS is based on three novel techniques namely PG-LAPS, PG-GAPS, and RepSubset, that generate interpretable explanations of the preserved local and global structures in embeddings. In the first two techniques, the VisExPreS system proactively guides users during every step of the analysis. We demonstrate the utility of VisExPreS in interpreting, analyzing, and evaluating embeddings from different dimensionality reduction algorithms using multiple case studies and an extensive user study.