Code repair is a fundamental task in software development, facilitating efficient bug resolution and software maintenance. Although large language models (LLMs) have demonstrated considerable potential in automated code repair, their ability to comprehend and leverage diverse types of feedback, which is crucial for iterative self-correction in authentic debugging scenarios, remains insufficiently understood. To bridge this gap, we introduce FeedbackEval, a systematic benchmark constructed from three heterogeneous sources (HumanEval, CoderEval, and SWE-Bench-verified), to evaluate LLMs' feedback comprehension and code repair performance. We conduct a comprehensive empirical study on five state-of-the-art LLMs, including GPT-4o, Claude-3.5, Deepseek-R1, GLM-4, and Qwen2.5, to evaluate their behavior under both single-iteration and iterative code repair settings. Our results show that mixed feedback yields the highest repair success (63.6%), with LLM-Expert and test feedback providing strong targeted gains (62.9% and 57.9%, respectively), while minimal (53.1%) and compiler feedback (49.2%) offer moderate benefits and LLM-Skilled proves least effective (48.8%). Iterative feedback further enhances repair performance, though the marginal benefit diminishes after two or three iterations. Moreover, prompt structure is shown to be critical: structured reasoning (RR, CoT) and dynamic example selection deliver notable improvements, whereas removing semantic cues such as docstrings or role-play causes severe degradation. This work introduces a robust benchmark and delivers practical insights to advance the understanding and development of feedback-driven code repair using LLMs.