Responsive Web Design is the coding that allows a web page to be viewed well on any size screen. When viewing a website the code will recolonize your display size and render code to provide you with the best viewing. Some elements will resize (like photos) and text blocks will resize. The header and navigation will also be resized and or moved to an alternate location.
In today’s internet world, all websites need to be responsive. Current statistics show fifty percent or more visitors to a website are using a mobile device. This statistics is only likely to go up. If your website is not responsive and built for normal computer screens, mobile viewers will not have a pleasant experience. They will need to do a lot of scrolling left and right just to read your text. Many parts of your web page may not be seen at all.
Another reason your website needs to be responsive is search engines. More and more Google (and other search engines) is penalizing websites that are not responsive. This alone is a good reason to have a Responsive Web Design.