In this study, we present an interpretable deep learning framework for the early detection of breast cancer using quantitative features extracted from digitized fine needle aspirate (FNA) images of breast masses. Our deep neural network, using ReLU activations, the Adam optimizer, and a binary cross-entropy loss, delivers state-of-the-art classification performance, achieving an accuracy of 0.992, precision of 1.000, recall of 0.977, and an F1 score of 0.988. These results substantially exceed the benchmarks reported in the literature. We evaluated the model under identical protocols against a suite of well-established algorithms (logistic regression, decision trees, random forests, stochastic gradient descent, K-nearest neighbors, and XGBoost) and found the deep model consistently superior on the same metrics. Recognizing that high predictive accuracy alone is insufficient for clinical adoption due to the black-box nature of deep learning models, we incorporated model-agnostic Explainable AI techniques such as SHAP and LIME to produce feature-level attributions and human-readable visualizations. These explanations quantify the contribution of each feature to individual predictions, support error analysis, and increase clinician trust, thus bridging the gap between performance and interpretability for real-world clinical use. The concave points feature of the cell nuclei is found to be the most influential feature positively impacting the classification task. This insight can be very helpful in improving the diagnosis and treatment of breast cancer by highlighting the key characteristics of breast tumor.