Despite the Graph Neural Networks' (GNNs) proficiency in analyzing graph data, achieving high-accuracy and interpretable predictions remains challenging. Existing GNN interpreters typically provide post-hoc explanations disjointed from GNNs' predictions, resulting in misrepresentations. Self-explainable GNNs offer built-in explanations during the training process. However, they cannot exploit the explanatory outcomes to augment prediction performance, and they fail to provide high-quality explanations of node features and require additional processes to generate explainable subgraphs, which is costly. To address the aforementioned limitations, we propose a self-explained and self-supervised graph neural network (SES) to bridge the gap between explainability and prediction. SES comprises two processes: explainable training and enhanced predictive learning. During explainable training, SES employs a global mask generator co-trained with a graph encoder and directly produces crucial structure and feature masks, reducing time consumption and providing node feature and subgraph explanations. In the enhanced predictive learning phase, mask-based positive-negative pairs are constructed utilizing the explanations to compute a triplet loss and enhance the node representations by contrastive learning.