The term "retina display" is a hardware term coined by Apple in June, 2010. It describes a display that has a resolution of over 300 dpi. The iPhone 4, which was also announced in June, 2010, has a screen resolution of 326 dpi and was the first Apple product to include a retina display.
The name "retina display" refers to way the high-resolution display appears to the human eye. When a display has a resolution over 300 dpi, most humans cannot recognize individual pixels when viewing the screen from a distance of about 12 inches. Therefore, the pixels seem to run together, creating a smooth appearance. This is similar to digital audio that is recorded with a high sampling rate. Since the audio samples are so close together, we perceive the sound as a smooth analog signal.
Since some people have better vision than others, there is no scientifically accurate number that defines a retina display. In fact, some people may in fact be able to identify individual pixels in a retina display. Still, compared to a typical computer monitors, which has a resolution of 72 dpi, a retina display will look noticeably sharper to all users.
Retina displays are especially useful for reading text on a small screen, such as an iPhone or iPod Touch. The increased resolution makes small text legible and medium-sized text easier to read. As display technology continues to evolve, retina displays are expected to be made available in larger devices, such as the iPad and HiDPI monitors.