Mobile first
Mobile first means you design for the phone screen first, then make it bigger for computers.
In a simple example
You start with one column, big buttons and short text, then let the layout spread out on a wide screen.
Why it matters to you
Most of your visitors hold a phone, so the phone view is the one that counts most.
Do not confuse with
Mobile first is a way of working. Responsive is the result you get at the end.