Browser compatibility is the concern in web site development that specific pages or sites work correclty in multiple web browsers.
Browser compatibility is a concern in web site design and development as to whether a web page or web site works correctly in different web browsers, and how the web pages are rendered, or displayed, in those different browsers.
Different people use different web browsers for a variety of reasons. These web browsers have different capabilities and varying strengths and weaknesses. Insuring that your web site is compatible allows your site visitors to experience your web site regardless of what web browser they are using, or what operating system they have on their computer.
Insuring that your web site works for all users will increase satisfaction and will help with search engine optimization, since the search engine spiders are just another variety of web browser.