Describe the fundamental relationship between bond prices and yields. What are the key factors that influence both bond prices and yields? Additionally, explain your understanding of the yield curve and its role in fixed income market analysis.

你如何理解债券价格与收益率之间的基本关系？请进一步阐述影响债券价格和收益率的关键因素有哪些。此外，请简要谈谈你对收益率曲线基本概念的理解，以及它在固定收益市场分析中扮演着怎样的角色。