The growing demand for transparency and interpretability in critical domains has driven increased interests in comprehending the explainability of Message-Passing (MP) Graph Neural Networks (GNNs). Although substantial research efforts have been made to generate explanations for individual graph instances, identifying global explaining concepts for a GNN still poses great challenges, especially when concepts are desired in a graphical form on the dataset level. While most prior works treat GNNs as black boxes, in this paper, we propose to unbox GNNs by analyzing and extracting critical subtrees incurred by the inner workings of message passing, which correspond to critical subgraphs in the datasets. By aggregating subtrees in an embedding space with an efficient algorithm, which does not require complex subgraph matching or search, we can make intuitive graphical explanations for Message-Passing GNNs on local, class and global levels. We empirically show that our proposed approach not only generates clean subgraph concepts on a dataset level in contrast to existing global explaining methods which generate non-graphical rules (e.g., language or embeddings) as explanations, but it is also capable of providing explanations for individual instances with a comparable or even superior performance as compared to leading local-level GNN explainers.