A lot of font-icons allow you to set the the icon using class names. So rather than linking to a specific image file or using some obscure ascii code like in the stackoverflow example you linked to, I can just add a class name like 'icon-user' and the user icon will show up. It's definitely easier in some situations.

Font icons are scalable too, which makes it really easy to change the icon size on the fly. Since I do all of my development directly in the browser, I never know how big I need my icons until I've done some experimenting with different sizes. Font icons make this experimentation process a lot easier because I don't need to update an image file. I can just change the font-size property in css.