If news reports last week are to be believed, Apple has invented a transparent phone! Quite where all the electronics and the battery were going to hide, I don't know...
On closer inspection, upon reading the granted patent claims (which define the legal monopoly obtained by Apple), they have a number of claims directed to a "display" and an "electronic device" having a flexible (e.g. OLED) substrate for the display, with the substrate having an opening behind which is located an electronic component. The opening is able to transmit signals through to the electronic component.
The dependent claims of the patent (which describe optional and preferable features of the main invention) set out that the electronic component could be a light sensor, a speaker, a microphone or an antenna, for example. It would therefore appear that Apple is looking to embed some sort of sensor or other component behind the display screen (e.g. to be surrounded by display pixels). However the opening in the display screen would allow the electronic component to receive the signals that it needs to operate. An OLED display would appear to allow this to be achieved (which may not be technically possible using a traditional LED/LCD display).
In the description of the patent (but not defined in the claims) it also talks about using this opening in the screen to view objects through. This would appear to be where all the hype over the transparent iPhone came from! The patent describes that such a transparent area could also display some information to form a "head-up" display. This could be used to display augmented reality features.
Apple is granted thousands of patents a year for a wide variety of different inventions. While some may give an insight into features of products that are yet to be released, others may be ideas that get left on the cutting room floor. We will have to wait until the next (or even later) iPhone is released to see what actually becomes reality.
So it comes down to aesthetics and the ability to remove the screen bezel by embedding the components that are currently in the bezel -- specifically light sensors, the front-facing camera, and the earpiece speaker -- directly into the display.