Though many deep learning (DL)-based vulnerability detection approaches have been proposed and indeed achieved remarkable performance, they still have limitations in the generalization as well as the practical usage. More precisely, existing DL-based approaches (1) perform negatively on prediction tasks among functions that are lexically similar but have contrary semantics; (2) provide no intuitive developer-oriented explanations to the detected results. In this paper, we propose a novel approach named SVulD, a function-level Subtle semantic embedding for Vulnerability Detection along with intuitive explanations, to alleviate the above limitations. Specifically, SVulD firstly trains a model to learn distinguishing semantic representations of functions regardless of their lexical similarity. Then, for the detected vulnerable functions, SVulD provides natural language explanations (e.g., root cause) of results to help developers intuitively understand the vulnerabilities. To evaluate the effectiveness of SVulD, we conduct large-scale experiments on a widely used practical vulnerability dataset and compare it with four state-of-the-art (SOTA) approaches by considering five performance measures. The experimental results indicate that SVulD outperforms all SOTAs with a substantial improvement (i.e., 23.5%-68.0% in terms of F1-score, 15.9%-134.8% in terms of PR-AUC and 7.4%-64.4% in terms of Accuracy). Besides, we conduct a user-case study to evaluate the usefulness of SVulD for developers on understanding the vulnerable code and the participants' feedback demonstrates that SVulD is helpful for development practice.