Skin cancer is a severe and potentially lethal disease, and early detection is critical for successful treatment. Traditional procedures for diagnosing skin cancer are expensive, time-intensive, and necessitate the expertise of a medical practitioner. In recent years, many researchers have developed artificial intelligence (AI) tools, including shallow and deep machine learning-based approaches, to diagnose skin cancer. However, AI-based skin cancer diagnosis faces challenges in complexity, low reproducibility, and explainability. To address these problems, we propose a novel Grid-Based Structural and Dimensional Explainable Deep Convolutional Neural Network for accurate and interpretable skin cancer classification. This model employs adaptive thresholding for extracting the region of interest (ROI), using its dynamic capabilities to enhance the accuracy of identifying cancerous regions. The VGG-16 architecture extracts the hierarchical characteristics of skin lesion images, leveraging its recognized capabilities for deep feature extraction. Our proposed model leverages a grid structure to capture spatial relationships within lesions, while the dimensional features extract relevant information from various image channels. An Adaptive Intelligent Coney Optimization (AICO) algorithm is employed for self-feature selected optimization and fine-tuning the hyperparameters, which dynamically adapts the model architecture to optimize feature extraction and classification. The model was trained and tested using the ISIC dataset of 10,015 dermascope images and the MNIST dataset of 2357 images of malignant and benign oncological diseases. The experimental results demonstrated that the model achieved accuracy and CSI values of 0.96 and 0.97 for TP 80 using the ISIC dataset, which is 17.70% and 16.49% more than lightweight CNN, 20.83% and 19.59% more than DenseNet, 18.75% and 17.53% more than CNN, 6.25% and 6.18% more than Efficient Net-B0, 5.21% and 5.15% over ECNN, 2.08% and 2.06% over COA-CAN, and 5.21% and 5.15% more than ARO-ECNN. Additionally, the AICO self-feature selected ECNN model exhibited minimal FPR and FNR of 0.03 and 0.02, respectively. The model attained a loss of 0.09 for ISIC and 0.18 for the MNIST dataset, indicating that the model proposed in this research outperforms existing techniques. The proposed model improves accuracy, interpretability, and robustness for skin cancer classification, ultimately aiding clinicians in early diagnosis and treatment.