Person Re-identification (ReID) has achieved significant improvement due to the adoption of Convolutional Neural Networks (CNNs). However, person ReID systems only provide a distance or similarity when matching two persons, which makes users hardly understand why they are similar or not. Therefore, we propose an Attribute-guided Metric Interpreter, named AttriMeter, to semantically and quantitatively explain the results of CNN-based ReID models. The AttriMeter has a pluggable structure that can be grafted on arbitrary target models, i.e., the ReID models that need to be interpreted. With an attribute decomposition head, it can learn to generate a group of attribute-guided attention maps (AAMs) from the target model. By applying AAMs to features of two persons from the target model, their distance will be decomposed into a set of attribute-guided components that can measure the contributions of individual attributes. Moreover, we design a distance distillation loss to guarantee the consistency between the results from the target model and the decomposed components from AttriMeter, and an attribute prior loss to eliminate the biases caused by the unbalanced distribution of attributes. Finally, extensive experiments and analysis on a variety of ReID models and datasets show the effectiveness of AttriMeter.