Mobile first
In the early days of emerging mobile access to the web, with small screens and it being difficult to type into, the general philosophy of mobile provision was for a separate mobile site containing a cut down version of the content. In the modern era with much improved displays and capabilities of modern phones, plus the mass market penetration of intermediate devices such as tablets, we can no longer assume that mobile users only want to carry out web activity when on the move away from home, and we can confidently provide a richer experience to mobile users than previously. You will know from your own analytics for your own site, but it's highly likely they will show at least 50% of your site accesses are from a mobile device..
A mobile first strategy means we adopt an assumption all information and functionality that users need to carry out can be accessed on a reasonably mid-specification modern touchscreen smartphone. If they are unable to complete the whole of the task on their mobile device, the page needs to give them sufficient information to reassure them that this is the correct page to come back to in order to transfer to the desktop environment at their convenience, ideally they would be able to hand off the progress they've made on their mobile device to the larger screen without having to start again from the beginning – thus, the visitor should be able to gain some value from having visited the page on their mobile device, with added value for those who have visited on the desktop.
A mobile first strategy also means when you are designing layouts, UX designs, and the graphic design, you create and test your initial designs for a mobile view with the widescreen / desktop view being the secondary design, rather than yesteryear's practice of designing for the desktop and creating the mobile layout as an afterthought.