Before launch, Sony promised that the PlayStation 4 would be able to resume a game as soon as you picked up the controller. However, the feature was pulled just before launch. The next 2.50 update will finally enable it.
Resume games in seconds
Sony calls is “Suspend/Resume”. Think of it like a quick start mode that lets you jump straight into the game you were playing before leaving your PlayStation 4 the last time.

As soon as you pick up the controller and press the “PS button” you can start playing the same game that you were playing before you put your PS4 to sleep. You just have to remember to put the PS4 in rest mode. Sony says that “Suspend/Resume” will be supported by nearly all PS4 games.
The 2.50 update will also increase Remote / Share Play to 60 frames per second for smoother playback, and add some other minor features. The 2.50 update is not available yet, but will be soon, according to Sony.
- Source: PlayStation.Blog