Skin cancer is considered to be the most common human malignancy. Around 5 million new cases of skin cancer are recorded in the United States annually. Early identification and evaluation of skin lesions are of great clinical significance, but the disproportionate dermatologist-patient ratio poses a significant problem in most developing nations. Therefore a novel deep architecture, named as SkiNet, is proposed to provide faster screening solution and assistance to newly trained physicians in the process of clinical diagnosis of skin cancer. The main motive behind SkiNet's design and development is to provide a white box solution, addressing a critical problem of trust and interpretability which is crucial for the wider adoption of Computer-aided diagnosis systems by medical practitioners. The proposed SkiNet is a two-stage pipeline wherein the lesion segmentation is followed by the lesion classification. Monte Carlo dropout and test time augmentation techniques have been employed in the proposed method to estimate epistemic and aleatoric uncertainty. A novel segmentation model named Bayesian MultiResUNet is used to estimate the uncertainty on the predicted segmentation map. Saliency-based methods like XRAI, Grad-CAM and Guided Backprop are explored to provide post-hoc explanations of the deep learning models. The ISIC-2018 dataset is used to perform the experimentation and ablation studies. The results establish the robustness of the proposed model on the traditional benchmarks while addressing the black-box nature of such models to alleviate the skepticism of medical practitioners by incorporating transparency and confidence to the model's prediction.