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Constructing a high-quality dense map in real-time is essential for robotics, AR/VR, and digital twins applications. As Neural Radiance Field (NeRF) greatly improves the mapping performance, in this paper, we propose a NeRF-based mapping method that enables higher-quality reconstruction and real-time capability even on edge computers. Specifically, we propose a novel hierarchical hybrid representation that leverages implicit multiresolution hash encoding aided by explicit octree SDF priors, describing the scene at different levels of detail. This representation allows for fast scene geometry initialization and makes scene geometry easier to learn. Besides, we present a coverage-maximizing keyframe selection strategy to address the forgetting issue and enhance mapping quality, particularly in marginal areas. To the best of our knowledge, our method is the first to achieve high-quality NeRF-based mapping on edge computers of handheld devices and quadrotors in real-time. Experiments demonstrate that our method outperforms existing NeRF-based mapping methods in geometry accuracy, texture realism, and time consumption. The code will be released at: https://github.com/SYSU-STAR/H2-Mapping