Responsive design, or sometimes called mobile ready or mobile friendly, is when a website is able to rescale or rearrange elements, images, buttons, etc to be viewed and interacted with on different size screens. These screen sizes typically begin to take advantage of a responsive site on tablet sizes all the way down to mobile devices.
Responsive design is not a mobile theme or an app. Responsive design ignores the devices and only responds to the pixel dimensions of the screen reading the theme. Mobile themes were popular back around 2012 as an economical way to have a mobile friendly site. Most mobile themes are not friendly and tend to take a site design and turn it into a flat, mapped interface.