This study progresses solar flare prediction research by presenting a full-disk deep-learning model to forecast $\geq$M-class solar flares and evaluating its efficacy on both central (within $\pm$70$^\circ$) and near-limb (beyond $\pm$70$^\circ$) events, showcasing qualitative assessment of post hoc explanations for the model's predictions, and providing empirical findings from human-centered quantitative assessments of these explanations. Our model is trained using hourly full-disk line-of-sight magnetogram images to predict $\geq$M-class solar flares within the subsequent 24-hour prediction window. Additionally, we apply the Guided Gradient-weighted Class Activation Mapping (Guided Grad-CAM) attribution method to interpret our model's predictions and evaluate the explanations. Our analysis unveils that full-disk solar flare predictions correspond with active region characteristics. The following points represent the most important findings of our study: (1) Our deep learning models achieved an average true skill statistic (TSS) of $\sim$0.51 and a Heidke skill score (HSS) of $\sim$0.38, exhibiting skill to predict solar flares where for central locations the average recall is $\sim$0.75 (recall values for X- and M-class are 0.95 and 0.73 respectively) and for the near-limb flares the average recall is $\sim$0.52 (recall values for X- and M-class are 0.74 and 0.50 respectively); (2) qualitative examination of the model's explanations reveals that it discerns and leverages features linked to active regions in both central and near-limb locations within full-disk magnetograms to produce respective predictions. In essence, our models grasp the shape and texture-based properties of flaring active regions, even in proximity to limb areas -- a novel and essential capability with considerable significance for operational forecasting systems.