When a website is responsive, the layout and/or content responds (or, adapts) based on the size of the screen it’s presented on.
A responsive website automatically changes to fit the device you’re reading it on.
Typically, there have been four general screen sizes that responsive design has been aimed at: the widescreen desktop monitor, the smaller desktop (or laptop), the tablet, and the mobile phone.
As you can see in the examples below, as the screen gets smaller, the content shifts and changes to the best display for each screen …
In short, you (the digital publisher, developer, and designer) should care because you want the visitors to your website to have the best experience possible, without forcing them to adapt themselves.
There are essentially two ways you can give your audience a good experience utilizing responsive design: