Beaner, at its most basic description, it's a design technique that auto scales to the current viewport of the end user. Images, css containers, etc. scale while legibility remains.
Thus, you basically see the same site on a Desktop PC / Mac as you would on a tablet as you would on a smart phone, etc. Obviously it reaches a point where you need to specify a minimum viewing width, but at the point, each section begins to "stack" on top of one another (for example... if you have two lead features side by side... they will scale down to fit inside a user's viewport until a specific point, then it will auto render with one feature above the other.
Here's a Wikipedia Link:
http://en.wikipedia.org/wiki/Responsive_web_design
Here's a good example:
http://mashable.com/2012/12/11/responsive-web-design/
With your cursor on the right edge of the window... drag it towards the left to make your screen width smaller. You can see the design "respond" to the current viewing width without forcing you to scroll sideways.