Responsive web design is a recent term to define the technique of designing websites which can be viewed on different formats of devices.
This kind of websites can display its content according the size of the screen of computer, tablets or phones. The way it can happen is designing all the content in a fluid grid that changes in vertical o horizontal.
Recently, Google is motiving to the companies to do it so they can index easily websites.
The main advantage of responsive web design is to asure you website is going to be displayed in all devices without affecting the user experience in your audience.