Responsive web design means that a website is shown properly, no matter if you surf the Internet from a PC, a tablet or a smartphone. Responsive web design is a MUST nowadays, where surfing the Internet from a smartphone becomes more and more common.
If the website is not responsive, surfers must scroll horisontally and zoom in and out constantly. Links are often so small that they are not easy to click and not user friendly at all. If you check a website from a PC, just make the screen size smaller horizontally and you can check if the website you are visiting is responsive.
Above you see how a website looks on a PC. Below is how the same website looks on a smartphone:
No matter who you choose to create your new website, make sure that your new design is made responsive.