Mobile First
The mobile-first approach is a tenet of progressive enhancement. It is the ideology that mobile design, as the hardest, should be done first. Once the mobile design questions are answered, designing for other devices will be easier.
If your site is good on a mobile device, it translates better to all devices. More important, though, is that the mobile-first approach is also a content-first approach. Mobile has the most limitations, screen size and bandwidth to name a few, and so designing within these parameters force you to prioritize content ruthlessly.
The mobile-first approach organically leads to a design that’s more content-focused, and therefore user-focused. The heart of the site is content — that’s what the users are there for.
And since Google is the divine being you’re trying to impress with your website, it is wise to pay attention to what Google loves. Google not only recommends responsive websites as the best way to target mobile users, but also favors mobile-optimized sites when presenting results for searches made on a mobile device. This is especially true when mobile users search for local services.