The reason that progressive enhancement is great is because your website will work well across all browsers and devices, unlike graceful degradation– which creates websites for the newest and most capable browsers (first). Progressive enhancement does not worry about browsers, it is solely concerned with the content of the site and making sure that it is correct by layering the different elements (in the correct order) that make the website viewable.
Progressive enhancement is the way to build a website, because then you do not have to worry about rebuilding the site to work with a certain browser, and you can reach a wide variety of people / audience because you can let people with older browsers view your site. As developers, we want to be able to create things for everyone to see from the start!
Here is another interesting article about Progressive Enhancement.