Refers to the physical number of pixels displayed on a screen (such as 1280×1024). Unlike in print, display resolution does not refer to the number of pixels or dots per inch on a computer screen, as this can be changed by changing the resolution of the screen (which, of course, does not change the physical size of the screen). The resolution of an image, however, is often referred to in terms of pixels per inch, though this has very little effect on how the image is displayed on screen.
A responsive (mobile responsive) website has a layout that resizes and readjusts based on the size of the screen it's being viewed on. This means whether someone is viewing your site on a mobile device or a 30" screen they're getting the same experience, and your website is being server up perfectly to them.