The mobile first approach to web design asserts not only that the mobile experience of a web site should be considered and not merely an afterthought but should have priority: design should first be for smaller (presumably mobile) viewports and the experience can then be enhanced for larger viewports. Tim Kadlec (Implementing Responsive Design: Building sites for an anywhere, everywhere web, 2012, pp. 74-75) reports that most sites are still (2012) designed for the desktop viewport then down but that they should be designed for mobile viewports then up.
Here’s Ethan Marcotte on the mobile first approach (Marcotte, Responsive Web Design, 2011, p. 113):
It’s all too easy to fill a desktop browser window with social media toolbars, links to related articles, battalions of RSS links, and tag clouds galore. (This process is called adding value, I believe.) But when we’re forced to work with a screen that’s 80% smaller than our usual canvas, nonessential content and cruft quickly fall away, allowing us to focus on the truly critical aspects of our designs.
In other words, designing for mobile devices first can enrich the experience for all users, by providing the element often missing from modern web design: focus. That’s not to say that our client’s pages are light on content, or lacking in features. But by framing our design process with that simple question [How does this content or feature benefit our mobile users?], we’ve gained a handy acid test to apply when considering each proposed element, each new piece of functionality (brackets not in Marcotte).