The web world changed way back in 2010 with the common usage of cell phones and the internet. A responsive website means one the will size up or down to whatever viewing device one is using. To quote Wikipedia...
Responsive web design (RWD) is an approach to web design aimed at crafting sites to provide an optimal viewing experience—easy reading and navigation with a minimum of resizing, panning, and scrolling—across a wide range of devices (from desktop computer monitors to mobile phones).
Back in the old days, websites had a fixed width regardless of the device being used, so one had to scroll back and forth on a phone to read a blog and could only look at a portion of a website. That all changed in about two years around 2010, when responsive websites became more and more common.
Today we only build responsive sites unless there is a reason not too. It has been another learning curve to adapts to the flexible values needed to create responsive sites, but that is the nature of the business. It also affects the design of websites, creating layouts to scale down to a phone width and rearrange itself accordingly - think about a bunch of boxes aligning hroizontally, then realigning vertically for a narrower fit.
For more reading - http://smallbiztrends.com/2013/05/what-is-responsive-web-design.html