Three-dimensional (3D) local feature description is an important research direction in 3D computer vision, widely used in many tasks of 3D perception to obtain point correspondences between two point clouds. Addressing the issues of low descriptiveness and weak robustness in existing descriptors, we propose a local divisional attribute statistical histogram (LDASH) descriptor. The LDASH descriptor is constructed based on local reference axes (LRA). First, the local space is partitioned radially, and then five feature attributes are computed within each partition, comprehensively encoding spatial and geometric information. In LDASH descriptor, we introduce a new attribute called distance weighted angle value (DWAV) for local feature description. DWAV is not dependent on LRA, thus enhancing the descriptor's robustness against LRA errors. Furthermore, a robustness enhancement strategy is proposed to reduce the interference of point cloud resolution variations in practical testing on the descriptors. The performance of the LDASH descriptor is extensively evaluated on six datasets with different application scenarios and interference types. The results demonstrate that LDASH descriptor outperforms existing descriptors in all datasets. Compared to the second-best method (divisional local feature statistics descriptor), LDASH descriptor exhibits an average improvement of approximately 16.3% in discriminability and 7.5% in robustness. Finally, LDASH descriptor is applied to point cloud registration, achieving a correct registration rate of 73% when combined with the five transformation estimation algorithms.