In a nutshell, responsive design or responsive build refers to ability of a web page to rearrange its elements depending on screen size of device being used. It is an evolution of HTML coding from creating desktop and mobile versions of the site to a single build that presents appropriate layout regardless of user's browsing device. As such, it is a very good thing to happen for everyone involved in the creative and development process of online work.
The inevitable curve for learning to both design and build responsive has to do with a shift from the idea of fixed layouts, which should be executed as a pixel match across browsers and platforms, to the concept of rules that page layout has to follow when rearranging content depending on size of the browser window. Responsive layouts, with 3 or more for each web page (for small, medium, and large browser sizes) represent a set of rules that page follows at that particular browser size. As the browser changes dimensions a different set of rules kicks in, and so the primary content stacks, secondary content disappears, and page always presents most relevant content in best possible layout for current browser window.
Building responsive takes longer for the creatives, who now have to create multiple layouts where before one could suffice, and for developers who spend additional time on specifically coding for responsive build. The benefit comes at the very end, when website performs across browsers and devices, not tied to particular screen size or device rotation - a term we didn't even consider a few years back. As Apple increasingly begins to share tablet and phone markets with Android devices, responsive builds that accommodate an increasingly wide range of devices will transition from being an option to a firmly established standard.