Responsive web design or (RWD) is specific techniques and code that allows a website to display differently depending upon what type of device it is being viewed on without using a totally different set of html instructions. In other words, a responsive website will generally look the same no matter what device is used to view it. Or as the Wikipedia article puts it:
"Responsive Web Design (RWD) is an approach to web design in which a site is crafted 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)."
Take a look at the picture below that we created to help explain this type of website. If you just give it a passing glance, the site looks the same on all of the devices pictured, however if you look closely you will see that each device displays the site slightly differently. In the full desktop version you see a very detailed slideshow and navigation. In the tablet version you see a smaller slideshow and limited navigation (it is seen below the text out of frame), but the same content. In the mobile versions the slideshow is even smaller, but the image has been resized and some of the text has been removed so that only the main title of the slide is visible. There are other more nuanced details that typically only impress geeks so i wont get into them here, but suffice it to say that it is very cool. It also makes your life easier because you don't have to worry about how someone is viewing your website... it doesn't matter, it will always look good. In addition, you don't have to add content more than once for this to happen.
This new technique has been developed thanks to HTML5 - or more specifically CSS3. If you don't know what those are, don't worry, you really shouldn't have to... that's why we are Your-Web-Guys. We keep up with that kind of stuff so you don't have to. Take a look at more information about responsive web design and some of the websites we have built using this new technique.