Mobile first is web development from the ground up. such as building a site that can be viewed in a smartphone or rather mobile device, then a tablet and finally the desktop. Its a much more efficient method then converting an enterprise site into responsive web design (RWD), which could lead to many sleepless nights due to coding errors.
Sites that are content based are much more easier to convert to responsive web design versus sites that entail a heavy amount of graphical content or rather graphics. Because being responsive would mean having the ability to swap out different sizes of graphics depending on the various break points that are established.
Something to keep in mind is that if a site can be viewed on a mobile device then most likely it can be viewed on the desktop. Excluding mobile applications etc. The reverse is Flash based websites and content cannot be viewed on an iPhone or iPad.