Q: What does that mean in a practical sense?
A: Potentially two things: images may be more vivid, and you may get better battery life.
AMOLED screens can be thinner, and naturally provide more vivid colors rather than the more realistic (and sometimes muddier looking) hues than on an LCD screen. These screens can also improve battery life or at least be more energy-efficient without the backlight.
That's particularly true when looking at dark colors, when an AMOLED screen can cut power to any pixel that should be black.
It's hard to say, however, how much battery life improvement you'll get on the new phone. Because an edge-to-edge screen means more screen real estate, Apple may be able to use energy savings from an OLED screen to offer a larger screen with the same battery life. Or it may be able to improve performance elsewhere in the phone. Apple declined to comment.
Q: Is Apple the first to use this kind of screen?
A: Nope. In fact, competitors such as Samsung and LG - both of which manufacture screens - have already put some kind of OLED on their smartphones. So if you want to see what the difference may look like, you can look at a phone such as the Galaxy S8 or the new LG V30, which has its own plastic variant of an OLED screen called POLED. (Yes, the "p" is for plastic.)
Q: How could this affect my relationship with the iPhone?
A: For one, it could make a dent in your wallet if you want the top-tier phone. Apple's current screens are cheaper to produce, which helps explain why analysts are expecting a big price bump for the most expensive iPhone.
There are some differences between the LCD and AMOLED screens on the market now. LCD screens tend to show more muted colors, but they're also generally truer to life. They can also be easier to see in direct sunlight and brighter than AMOLED screens, due to the backlight.
But with a sharper screen, those social media posts and streaming videos we all peruse on our phones will look better, as will emerging technologies such as augmented reality - another emerging Apple interest.