This refers to a way of coding a site so that it displays optimally on a mobile device as well as large screens. A RWD is comprised of breakpoints (typically 4), one for a mobile phone, tablet, desktop standard and desktop large. Read more about it here.
Responsive websites have become standard. 2 years ago there were less than 100 types of devices that could access the Internet, now there are close to 300. If you are redesigning your site make sure it uses a RWD.