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Recently, self-supervised instance discrimination methods have achieved significant success in learning visual representations from unlabeled photographic images. However, given the marked differences between photographic and medical images, the efficacy of instance-based objectives, focusing on learning the most discriminative global features in the image (i.e., wheels in bicycle), remains unknown in medical imaging. Our preliminary analysis showed that high global similarity of medical images in terms of anatomy hampers instance discrimination methods for capturing a set of distinct features, negatively impacting their performance on medical downstream tasks. To alleviate this limitation, we have developed a simple yet effective self-supervised framework, called Context-Aware instance Discrimination (CAiD). CAiD aims to improve instance discrimination learning by providing finer and more discriminative information encoded from a diverse local context of unlabeled medical images. We conduct a systematic analysis to investigate the utility of the learned features from a three-pronged perspective: (i) generalizability and transferability, (ii) separability in the embedding space, and (iii) reusability. Our extensive experiments demonstrate that CAiD (1) enriches representations learned from existing instance discrimination methods; (2) delivers more discriminative features by adequately capturing finer contextual information from individual medial images; and (3) improves reusability of low/mid-level features compared to standard instance discriminative methods. As open science, all codes and pre-trained models are available on our GitHub page: https://github.com/JLiangLab/CAiD.