User acceptance of artificial intelligence agents might depend on their ability to explain their reasoning, which requires adding an interpretability layer that fa- cilitates users to understand their behavior. This paper focuses on adding an in- terpretable layer on top of Semantic Textual Similarity (STS), which measures the degree of semantic equivalence between two sentences. The interpretability layer is formalized as the alignment between pairs of segments across the two sentences, where the relation between the segments is labeled with a relation type and a similarity score. We present a publicly available dataset of sentence pairs annotated following the formalization. We then develop a system trained on this dataset which, given a sentence pair, explains what is similar and different, in the form of graded and typed segment alignments. When evaluated on the dataset, the system performs better than an informed baseline, showing that the dataset and task are well-defined and feasible. Most importantly, two user studies show how the system output can be used to automatically produce explanations in natural language. Users performed better when having access to the explanations, pro- viding preliminary evidence that our dataset and method to automatically produce explanations is useful in real applications.