Outlier detection is an important task in many domains and is intensively studied in the past decade. Further, how to explain outliers, i.e., outlier interpretation, is more significant, which can provide valuable insights for analysts to better understand, solve, and prevent these detected outliers. However, only limited studies consider this problem. Most of the existing methods are based on the score-and-search manner. They select a feature subspace as interpretation per queried outlier by estimating outlying scores of the outlier in searched subspaces. Due to the tremendous searching space, they have to utilize pruning strategies and set a maximum subspace length, resulting in suboptimal interpretation results. Accordingly, this paper proposes a novel Attention-guided Triplet deviation network for Outlier interpretatioN (ATON). Instead of searching a subspace, ATON directly learns an embedding space and learns how to attach attention to each embedding dimension (i.e., capturing the contribution of each dimension to the outlierness of the queried outlier). Specifically, ATON consists of a feature embedding module and a customized self-attention learning module, which are optimized by a triplet deviation-based loss function. We obtain an optimal attention-guided embedding space with expanded high-level information and rich semantics, and thus outlying behaviors of the queried outlier can be better unfolded. ATON finally distills a subspace of original features from the embedding module and the attention coefficient. With the good generality, ATON can be employed as an additional step of any black-box outlier detector. A comprehensive suite of experiments is conducted to evaluate the effectiveness and efficiency of ATON. The proposed ATON significantly outperforms state-of-the-art competitors on 12 real-world datasets and obtains good scalability w.r.t. both data dimensionality and data size. This is the first work to release the ground-truth outlier interpretation annotations of real-world datasets.