The opacity of production information from various sensitive users in distribution networks makes it difficult to construct explicit functions to accurately quantify the impact of voltage sags on sensitive loads, thereby limiting the effectiveness of resilience enhancement strategies for distribution network operations. To address this issue, a data-physical hybrid-driven method is proposed for evaluating and enhancing distribution network operational resilience. By drawing analogies with traditional resilience indices and their definitions, a new operational resilience index that accounts for the impact of voltage sags on sensitive users is constructed. Considering the different tolerance characteristics of various sensitive users to voltage sags, a voltage sag trajectory characteristic system is established to represent the response characteristics of different sensitive loads. A data-driven model is then proposed to evaluate distribution network operational resilience. On this basis, the data-driven resilience evaluation process is embedded into a physical model for multi-objective energy storage optimization. Finally, a case study based on the IEEE33-bus distribution network is conducted. The results demonstrate that the proposed data-physical hybrid-driven model for energy storage optimization can address the challenge of explicitly modelling the functional relationship between voltage sag characteristics and resilience indices, and can enhance resilience evaluation results while ensuring economic operation of the distribution network.