A font serves three purposes:
I’m not talking about the actual words, this is purely focusing on the shape and expectations of the font.
a simple example is serif- v.s. a sans serif typeface. A serif type has strokes at the ends of a letter; A sans serif type does not. A serif font ‘feels’ more authoritative than a sans serif font. This could be because we are used to seeing this kind of font in news papers and important documents. 'The medium is the message' could also be 'The typeface is the message'. When you have the proper typeface for a message, it will be easier to deliver.
Technology has taken huge leaps forward when it comes to the screen, the images can be so crisp and clear there is hardly any difference between paper and screen. However, just because that technology is out there does not mean everyone uses it. When using typography for web, its still smart to use a type that is easy to read on an older screen.
These next two images should look similar in quality on a low resolution screen. On a high resolution screen the 2nd image will look bad.
The same goes for large slabs of text. When the font is skinny and tall your eyes will become tired. When a font is open and spacious its easier to read.
It’s almost always a bad idea to go crazy with the regular text, you don't want to scare people away by making it hard to read, but a headline can go bonkers! A headline can help an identity be distinctive and recognizable. It’s not ment to be really easy to read, it’s meant to attract and lure. The New Yorker and Wired magazine are good examples of using an eccentric font for their headlines.