It can mean many things. Depending of who asks.
“Many companies caught on to the mobile-first trend awhile back. Google surfaced their mobile-first strategy in 2010. As you’ve probably guessed from the name of this approach to site design, mobile first means designing an online experience for mobile before designing it for the desktop Web-or any other device. In the past, when users’ focus was on the desktop Web, mobile design was an afterthought. But today, more people are using their mobile devices for online shopping and social networking than ever before, and most companies are designing for mobile. Mobile first requires a new approach to planning, UX design, and development that puts handheld devices at the forefront of both strategy and implementation. The digital landscape has changed, and companies have realized that consumers are now accessing more content on their mobile devices than anywhere else.”
(Riley Graham a.k.a. @lrileygraham ~ UXmatters)