A “responsive” design is one that responds to the size of the screen it’s being viewed on and rearranges itself to best fit that screen. This allows a site to look good on a tablet, cell phone, or any size/aspect ratio of computer monitor.
For example, try resizing this window by grabbing a corner and moving it around a bit, changing the width of the screen. You’ll see the menus, text, and portfolio items move themselves around to better adapt to the various screen’s changing width.
Responsive design is a fairly recent development. In the past, to make a site visible on a cell phone people had to either shrink the site to the point it was unreadable or force viewers to scroll horizontally as well as vertically, which is very difficult to navigate.
If your site has a responsive design, though, there are no compromises. You have several layouts optimized for different sizes of cellphones, tablets, or monitors and the your screen picks the best layout for its width.
Your site must be responsive
Responsive layout is the future. Every site I do from now on will be made this way. This simply isn’t a world any more where you can assume your viewers are using traditional computers. If your site isn’t useful on a tablet or cell phone, your business is going to suffer. Insist on responsive design, no matter who you hire. Don’t let anyone sell it to you as a “value added” proposition. Rather, it’s an absolutely essential requirement for every web site that exists.