Multilingual Neural Machine Translation (NMT) models have yielded large empirical success in transfer learning settings. However, these black-box representations are poorly understood, and their mode of transfer remains elusive. In this work, we attempt to understand massively multilingual NMT representations (with 103 languages) using Singular Value Canonical Correlation Analysis (SVCCA), a representation similarity framework that allows us to compare representations across different languages, layers and models. Our analysis validates several empirical results and long-standing intuitions, and unveils new observations regarding how representations evolve in a multilingual translation model. We draw three major conclusions from our analysis, with implications on cross-lingual transfer learning: (i) Encoder representations of different languages cluster based on linguistic similarity, (ii) Representations of a source language learned by the encoder are dependent on the target language, and vice-versa, and (iii) Representations of high resource and/or linguistically similar languages are more robust when fine-tuning on an arbitrary language pair, which is critical to determining how much cross-lingual transfer can be expected in a zero or few-shot setting. We further connect our findings with existing empirical observations in multilingual NMT and transfer learning.