Parallax scrolling is a technique long used in computer graphics to create a 3D-like sense of depth in 2D scenes. Based on the multiplane camera technique used in traditional animation, it involves making a background image pass more slowly than foreground images, creating an illusion of distance.
It's basically an optical illusion that takes advantage of the way the human eye sees closer objects as larger and faster than things that are further away. Over the last decade or so, it's been used in responsive web design to help create a more seamless, immersive experience.