Responsive web design is making your layouts fit for any device Desktop PC to a Smart Phone. Since more and more people using smart phones and tablets to surf web this has become very important part of web design. Adobe Dreamweaver has changed their software to this approach has provided set of tools to make it easy. But if you know the basics you can do with all manually too.
Here's a site which shows great examples of Responsive Designs
Media Queries
If your site is related to social media or targeting younger audience then this is a must. You have to make your site layouts fit to any device like tablets or smart phones.
Now I'm redoing all my mains sites which is a painful and long boring task. But if you want to keep with current trends no other choice.