In the realm of software development, providing accurate and personalized code explanations is crucial for both technical professionals and business stakeholders. Technical professionals benefit from enhanced understanding and improved problem-solving skills, while business stakeholders gain insights into project alignments and transparency. Despite the potential, generating such explanations is often time-consuming and challenging. This paper presents an innovative approach that leverages the advanced capabilities of large language models (LLMs) to generate faithful and personalized code explanations. Our methodology integrates prompt enhancement, self-correction mechanisms, personalized content customization, and interaction with external tools, facilitated by collaboration among multiple LLM agents. We evaluate our approach using both automatic and human assessments, demonstrating that our method not only produces accurate explanations but also tailors them to individual user preferences. Our findings suggest that this approach significantly improves the quality and relevance of code explanations, offering a valuable tool for developers and stakeholders alike.