When most people visit a website, they don't care much about the graphics, they just go through the text content. This is because text is the major source of information. So while creating content you should take care of balancing the graphics and text. This is why typography is so important.
Typography is so important for designers and brands as you want to ensure you're choosing fonts that both invoke positive responses whilst still providing easy readibility.
Certain fonts are seen as more 'fun' and lighthearted fonts and some are seen as more professional. For example, Pinterest's branding is seen as a 'fun' font:
It is a more casual, scripted font that conveys friendliness and fun, which are the perfect emotions that the image pinning site likely wants to elicit from their primarily female, creative audience. Starting with 2011 Pinterest has been using a custom logotype designed by Juan Carlos Pagan in collaboration with Michael Deal. The closest font you can get is Terra Narrow Italic font for the 'P' and Bodoni Egyptian Pro Bold Ita font for the 'interest'.
The IT company Data Foundry use what is seen as a more professional, serious font. This is a more straightforward, modern font that evokes less emotion and conveys a more staunch tone, the perfect feel for an IT managed service company. I couldn't find the exact details of the company's logo to find out what font they use, but it looks like Tolyer No.1 Medium.
You need more than one font for your brand/website. If your brand relies more on image-based promotion (for example a fashion retailer), you mightn't need more than one font- but it never hurts.
Adding a second font often helps to provide visual cues to what information the text offers and increases the readability. In the instances where two fonts are used, companies typically use one font for headers and the other for body copy.