In Apple's recent financial filings, the company details a $4 billion purchase order with more than a year duration. This purchase order coincides with an "off-balance sheet obligation" for the same amount from the third quarter.
J.P. Morgan's analyst says that this order is related to Apple's long-term OLED sourcing deal from Samsung Display - probably for the next-gen OLED iPhone. J.P. Morgan further connects this order to a comment by Apple that it may have trouble acquiring troublesome components "on commercially reasonable terms". OLEDs indeed are currently supply-strained and Apple needed to make sure it has enough capacity.
We heard several reports that Apple is looking to switch its iPhone display from LCD to OLED in 2017 or 2018. In April 2015 Yonhap News reported that 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.
$2.6 billion was a rather low amount for 100 million 5.5" flexible OLED displays, and a $4 billion amount makes more sense ($40 per display). This is still just speculation by J.P. Morgan, though, of course...