Resolution is often the only specification quoted when referring to the finest of a digital image but there is actually much more to it than that. A five-inch 1280x720 image will look sharp and crisp on your phone but if you project it as 720p image in a movie theater, it would look horrible. This is where pixel density comes in. It is a measure of the resolution that also accounts for the size of the screen. PPI has become the most common way to denote pixel density although pixels per centimeter or PPC can also be used. To calculate PPI, simply measure 1 inch diagonally on the screen and then draw a line diagonally through them, and find out how many pixels it intersects with.
With older devices, there was tons of room for improvement. Diagonal lines look like stairs and circles even had an ugly staircase effect. However, this is improved in recent years and we've even begun to see this place where the eye cannot even pick out the individual pixels on the display. Once that point is reached, there's not much benefit to continuing to add cost and complexity to manufacturing because most people won't notice anyway.
Apple's branding for this good enough density concepts is retina but to determine if the display is retina there's one last thing to consider, “How far away are you going to be from the display.” IsThisRetina.com has a handy little tool for this and according to their calculator a 55 inch 1080p TV will have the same perceived pixel density from seven feet away as this 4.7 inch 1080p phone does from 7 inches away but there's more to a great display than how many pixels it has of course. Contrast, Color Accuracy, and Pixel Response Time influence the viewing experience tremendously.
Different display types can even affect other things like the battery life of your device, improving power efficiency, and panel technology. Panel technology also plays a large role. For example, while both the Samsung Galaxy S4 and the HTC One have 1080p display, the S4 uses as a PenTile matrix LED display that has fewer dots on it overall, while the One uses a more standard LCD display with RGB sub pixels.