Modeling dynamic interactions among network components is crucial to uncovering the evolution mechanisms of complex networks. Recently, spatio-temporal graph learning methods have achieved noteworthy results in characterizing the dynamic changes of inter-node relations (INRs). However, challenges remain: The spatial neighborhood of an INR is underexploited, and the spatio-temporal dependencies in INRs' dynamic changes are overlooked, ignoring the influence of historical states and local information. In addition, the model's explainability has been understudied. To address these issues, we propose an explainable spatio-temporal graph evolution learning (ESTGEL) model to model the dynamic evolution of INRs. Specifically, an edge attention module is proposed to utilize the spatial neighborhood of an INR at multi-level, i.e., a hierarchy of nested subgraphs derived from decomposing the initial node-relation graph. Subsequently, a dynamic relation learning module is proposed to capture the spatio-temporal dependencies of INRs. The INRs are then used as adjacent information to improve the node representation, resulting in comprehensive delineation of dynamic evolution of the network. Finally, the approach is validated with real data on brain development study. Experimental results on dynamic brain networks analysis reveal that brain functional networks transition from dispersed to more convergent and modular structures throughout development. Significant changes are observed in the dynamic functional connectivity (dFC) associated with functions including emotional control, decision-making, and language processing.