The Xbox One won't include a headset due to the inclusion of the new Kinect peripheral, Microsoft explained. Although the Xbox One does support a headset, which is sold separately, the reason it's not included is because the Kinect already comes bundled with the system, and has a built-in microphone to allow you to chat with friends.
"Xbox One does not include a pack-in headset accessory," Microsoft told Ars Technica. "Each Xbox One includes the new Kinect sensor, with a highly sensitive multi-array microphones designed to enable voice inputs and chat as a system-level capability, both in-game and with Skype and other experiences. For gamers who prefer a headset, we have a variety of offerings that you can find on the Xbox Wire."
Unfortunately, without a headset you'll be forced to hear other players' voices through your standard speakers, a real annoyance on the Xbox 360. The voices, when coming through the television, often sounded muddled when combined with the sounds of the gameplay. You are still able to purchase a Xbox One headset, though it will be sold separately. It's called the Xbox One Chat Headset and Microsoft has not announced pricing for it yet; though, they do have a description:
"A must-have for fans of online gaming, the new Xbox One Chat Headset, wired to the controller, is designed for long gaming sessions and clear voice chat. With a lightweight and comfortable new design, the mono chat headset features wideband digital audio and a unidirectional microphone. Gamers will love not having to take their hands off the controller to access the microphone mute and volume controls."
For comparison sake, the PS4 includes a basic mono earbud and microphone with each system. It also has a standard microphone jack while the Xbox One uses a proprietary jack.