Typography is the main thing which attracts the visitors to the website (of course after images). But the only reason visitors read the content and extract the actual knowledge of the website is through typography. If the typography in web design is functional, the usability of the website increase for the visitors and that change the visitors into regular clients or regular guests.
The typography should differ depending upon the content; but it is better if the typography is big, loud and easily readable. It helps the visitors to read easily, but every word on the website cannot be large and bold. So the designer should make sure that he writes on the major or main information in bold.
If you are still not clear about what type of typography you should use on your website then take a look at the below mentioned illustrations.
2-Stackoverflow Dev Days
5-Mark Boulton Design
8-Me In Motion