Apple will soon be introducing a new MFI (Made for iPhone) specification that will allow headphone manufacturers to make headphones using a Lightning connector instead of the standard 3.5mm jack.
Right now, the Lightning connector already supports audio in/out, which is how sound docks work, but to be able to make headphones for it, manufacturers need that particular specification from Apple which allows them to go forward.
The Lightning connector can output 48kHz lossless digital audio signal to the headphones and also accept 48kHz mono digital audio from the headphone mic. The Lightning port will provide power, which will take care of the power needs that the onboard DAC and amplifier these headphone will inevitably require (digital signal will need to be converted to analog and amplified before sending it to the speakers).
Once the specification is released, we will start seeing headphones with Lightning cables. Perhaps Apple will do away with the standard 3.5mm headphone jack completely (it’s thicker than the Lightning port and thus prevents the device from becoming slimmer) and maybe, since they acquired Beats, there will be a Beats headphone with Lightning connector before anyone else.
The Lightning audio support for headphones will arrive with a software update for existing iOS 7.1 devices.