The PS4 has a bunch of new features, but one of the coolest is the ability to automatically record gameplay video, take screenshots, and broadcast to Twitch or Ustream straight from your console. Take a look at this video for a look at all the features of the PS4's share button.
One note about using the share button to start recording: In the video I pointed out how you can change the share button settings. On that menu it says that you can double tap the button to begin a video clip. To stop the video clip, you need to open the share menu again (by a press or holding the button, depending on your setting).