Your PC almost certainly does include fonts with many Asian characters. When the web page includes characters that are not supported by the default font (such as Times or Verdana) you're using, browsers will automatically find an alternative font and use that instead, so that you still get readable text.
For Firefox, at least, there's a "fontinfo" add-on you can use to determine what font is actually being used to display any given piece of text - as it may not be the default font, or the font requested by CSS.
Web sites can use various techniques (including libraries like cufon or typeface.js, though CSS @font-face is usually a better option now that it's widely supported) to provide custom fonts for their pages, but this is not necessary in order for Asian text (for example) to be displayed on a typical PC.