Responsive Web Design is basically a design done with CSS3 Media Queries that changes according to the environment a visitor uses. In other words, the design "responds" to changes.
It may sound science-fictiony, but that's what happens. And it's not complicated like it sounds. It's actually easy to create a basic Responsive design. All you need to do is play a little with CSS3 Media Queries and setting different widths for container elements.