The Location-Based Social Networks (LBSN) (e.g., Facebook) have many factors (for instance, ratings, check-in time, etc.) that play a crucial role for the Point-of-Interest (POI) recommendations. Unlike ratings, the reviews can help users to elaborate their opinion and share the extent of consumption experience in terms of the relevant factors of interest (aspects). Though some of the existing recommendation systems have been using the user reviews, most of them are less transparent and non-interpretable. These reasons have induced considerable attention towards explainable and interpretable recommendation. To the best of our knowledge, this is the first paper to exploit the user reviews to incorporate the sentiment and opinions on different aspects for the personalized and explainable POI recommendation. In this paper, we propose a model termed as PERS (Personalized Explainable POI Recommender System) which models the review-aspect category correlation by exploiting deep neural network, formulates the user-aspect category bipartite relation as a bipartite graph, and models the explainable recommendation using bipartite core-based and ranking-based methods. The major contributions of this paper are: (i) it models users and locations based on the aspects posted by user via reviews, (ii) it exploits a deep neural network to model the review-aspect category correlation, (iii) it provisions the incorporation of multiple contexts (e.g., categorical, spatial, etc.) in the POI recommendation model, (iv) it formulates the preference of users' on aspect category as a bipartite relation, represents it as a location-aspect category bipartite graph, and models the explainable recommendation with the notion of ordered dense subgraph extraction using bipartite core-based and ranking-based approaches, and (v) it evaluates the generated recommendation with three real-world datasets.