Large language models (LLMs) have shown impressive performance in following natural language instructions to solve unseen tasks. However, it remains unclear whether models truly understand task definitions and whether the human-written definitions are optimal. In this paper, we systematically study the role of task definitions in instruction learning. We first conduct an ablation analysis informed by human annotations to understand which parts of a task definition are most important, and find that model performance only drops substantially when removing contents describing the task output, in particular label information. Next, we propose an automatic algorithm to compress task definitions to a minimal supporting set of tokens, and find that 60\% of tokens can be removed while maintaining or even improving model performance. Based on these results, we propose two strategies to help models better leverage task instructions: (1) providing only key information for tasks in a common structured format, and (2) adding a meta-tuning stage to help the model better understand the definitions. With these two strategies, we achieve a 4.2 Rouge-L improvement over 119 unseen test tasks.