Responsive web design is when you built a website that will automatically adjust its layout to fit whatever device is viewing it. This could be a Desktop computer or an Android Phone or iPhone. Most of this is handled using Media Queries on your CSS stylingsheet. Considering 65% of all traffic is going to come from mobile devices its important your site is easy to use on smaller screens. Its also important because as of April 21, 2015 google ranks mobile friendly websites higher for searches from mobild devices.