Responsive design allows you modify the layout, navigation, content, and appearance of a website or application based on the width of the user’s browser.
Example: This website uses responsive design — if you’re viewing it on a resizable browser (laptop/desktop), see what happens when you narrow the width of your browser. If you’re using a tablet browser or smartphone, try changing its orientation, e.g., from landscape to portrait. At the smallest screen sizes, the top navigation turns into a dropdown and multicolumn layouts become one column, all done through the magic of media queries and flexible layouts.
Some people think responsive design is the one-and-only answer to sites and applications for mobile users. Others believe it’s best to have separate websites or apps for different devices, e.g., iPad, smartphones, and laptops/desktops.
I’ll go with the classic usability answer: it depends.