'Cross-Browser Compatibility' is the capacity of a website, web application, HTML structure, or client-side script to operate effectively across various web browsers and devices. It aims to provide a consistent user experience for a web page or application, regardless of the browser used for access.

Challenges in achieving cross-browser compatibility stem from the discrepancies in how different browsers interpret code and render web pages. These variances often result from diverse levels of support for web standards (such as HTML, CSS, and JavaScript) and unique browser behaviors or bugs. Historically, developers faced considerable differences among prevalent browsers, necessitating specialized coding methods to ensure uniform behavior and appearance.

To achieve effective cross-browser compatibility, it's important to adhere to web standards and best practices. This ensures web content is accessible and functions well across various browsers. Strategies include testing websites on multiple browsers, implementing responsive design, and using progressive enhancement to offer a basic user experience, with more sophisticated features available on advanced browsers.

As web standards have evolved and browsers have become more compliant with these standards, cross-browser challenges have diminished. Nonetheless, browser-specific testing and optimization remain essential in web development to guarantee a consistent and inclusive user experience.

In sum, cross-browser compatibility is a fundamental aspect of web development. It ensures that web applications and sites are usable and accessible across the myriad of browsers and devices, thus reaching a broader audience.