How an OLED works:

Electricity runs through the OLED, which goes through the organic layers from the cathode to the anode.  The cathode gives electrons to the emissive layer while the anode removes electrons from the conductive layer.  Which is where the cathode gives electron holes to the conductive layer.  From there the electrons find these holes,  fills them and gives up energy as a photon of light causing the OLED emit to light.  Depending on the type of organic molecule in the emissive layer it will emit a certain color.  Each OLED has multiple types of organic films to make color display.  The amount of electricity running through it will affect the brightness of the light. (see ref #3: How Stuff Works, 2005)

the process
photo courtesy How stuff works