To elaborate on bradgrafelman's post, when you specify a url in an <a> tag that starts with a slash, this <a> tag is ultimately interpreted by somebody's browser. The URL in the <a> tag is interpreted by the browser relative to the domain from which the current document was loaded. E.g., if you go to example.com and see an HTML page with an <a> linking to /some/path/file.html then your browser, knowing that the domain is example.com, and seeing that the url starts with a slash, will interpret it as example.com/some/path/file.html.
When you use [man]require[/man] on your PHP script, then PHP will evaluate the file you have specified relative to the file system on the server. If your specified file starts with a slash, this means you have specified a full file path relative to the root of the server's file system. If your specified file path doesn't start with a slash, then PHP will search the current [man]include_path[/man] one directory at a time (in order) and will stop as soon as it finds a matching file.