Mobile-friendly (responsive) design means that each and every page automatically adapts or responds to the display size of the device being used to view the page; whether on a desktop, tablet, or phone.
The most important reason to be Mobile Friendly is that "Starting April 21, 2015, a website's mobile-friendliness will be considered as a Google Search ranking signal (Google)." In essence, non-responsive websites will be demoted in search results depending on the device used to perform the search.
These pages are an example of "responsive design" technology in action. To illustrate, try viewing this website on devices with different display sizes. If viewing on a desktop device, change the size of the browser window. These pages will adjust to the size of the viewer's window.
Another key is search engine visibility. There are many steps that go into ensuring visitors can find a website. Using key words in the website's page titles, embedding key words about a business within the text, registering website pages with Google and Bing, search engine follow up; all come into play to help make a website more visible.