Many web servers will have a ‘default document’ that is returned when you specify just a path and no file name. So browsing to http://example.com will return the default document from the document root directory of that domain.
Quite often the default document can be named index.html, index.htm or -if PHP is installed- index.php, but they can be other names as well, depending on the configuration.
Some sites are built up from many actual html files, while other, more dynamic sites usually look like they consist of many html pages, but actually they just have a single entry page (like index.php) that handles all requests and generates output based on the url.
HTML5 Boilerplate (assuming you mean this one) describes a structure for a site. This structure is mostly the build-up of HTML, CSS and JavaScript. The index.html included with it is only a skeleton HTML file. It describes what your output should look like. How that output is generated is up to you. You can create a big folder full of separate HTML files, or a dynamic site with a single entry point, like described above. The HTML5 document, the CSS and all the other front-end stuff are interpreted by the browser, and it doesn’t care how that content was generated.