In the site footer I see a link named “Enable/Disable Responsiveness”:
It looks like some text/images are scaled when Responsiveness is enabled, but what does actually it do?
On most websites, information is presented in different columns. On Stack Exchange, this is the left navigation, the main content like posts in the center and the different sidebars (Featured on Meta, Related Questions, Hot Network Questions) on the right. Responsiveness means that based on the screen size (usually the width), the different columns are displayed side by side, if there's enough room to make it work, and on top of each other if not: example. Also, on smaller widths some elements can be hidden altogether.
Disabling responsiveness simply means you're going back towards the 'old' version of the full site which didn't take screen sizes into account, at least not as much as the current version.