OLED is a new display technology, used to create thin, power efficient and bright displays. Today OLEDs are used in mobile phones, tablets, digital cameras and even TV sets - as OLEDs are considered the best display technology ever.
Apple and OLED displays
Apple has been playing around with OLED displays for years, filing for several OLED patents - mainly ones related to flexible OLEDs. In April 2015, Apple started to ship their first wearable device, the Apple Watch which uses a flexible AMOLED display (made by LG Display). OLED displays are especially suitable for wearable devices - as the displays are thinner and lighter than LCD displays, and are more power efficient (especially if you tweak the UI to suit the special OLED properties).
Several reports suggest that Apple will adopt OLEDs in future iPhones - in 2017 or perhaps 2018. ETNews reported that that Apple chose Samsung Display as the company's primary OLED supplier for its next-gen iPhone, and the two companies signed an official contract - with Flexible OLED supply for Apple's next iPhone to begin in 2017.
Yonhap News confirmed the story, and added some new details. This is still not official of course (SDC declined to comment), but according to Yonhap Samsung Display agreed to supply 100 million 5.5" AMOLED panels to Apple per year, for about $2.6 billion - with shipment starting to 2017. Apple will maintain this contract for at least three years.