Responsive web design (RWD) is an approach to building websites in order to provide the best viewing experience across a wide range of devices from desktop computer monitors to mobile phones.
A website built using this approach will adapt to make navigation of the site easier. The layout of the page will respond to fit the viewing area and orientation of the device in use. Elements such as banner carousels, which fill the page width of a desktop screen, can be replaced with smaller, more appropriate, images or carousels to suit a smaller screen such as a smart phone.
With Responsive Web Design there is only on version of the website. It is not necessary to maintain two, or more, versions of the website to serve to varying device types. The same content is served to all devices. Some code in the website decides what the most appropriate layout for the viewing device is and presents your content in the best possible manner.