Despite significant advancements in multirobot technologies, efficiently and collaboratively exploring an unknown environment remains a major challenge. In this paper, we propose AIM-Mapping, an Asymmetric InforMation enhanced Mapping framework based on deep reinforcement learning. The framework fully leverages the privileged information to help construct the environmental representation as well as the supervised signal in an asymmetric actor-critic training framework. Specifically, privileged information is used to evaluate exploration performance through an asymmetric feature representation module and a mutual information evaluation module. The decision-making network employs the trained feature encoder to extract structural information of the environment and integrates it with a topological map constructed based on geometric distance. By leveraging this topological map representation, we apply topological graph matching to assign corresponding boundary points to each robot as long-term goal points. We conduct experiments in both iGibson simulation environments and real-world scenarios. The results demonstrate that the proposed method achieves significant performance improvements compared to existing approaches.