PlayStation 4 users will be able to play games while the system checks for title updates and downloads them to the unit, according to Sony's massive FAQ for the console.
On PlayStation 3, the console would only check for patches upon attempting to boot up a game, and if one was available, users would have to exit to the system's XMB and wait for it to download and install before they could play. This was also the way it worked on Xbox 360.
On PS4, users can keep playing while a patch downloads in the background, although they'll still need to exit out to the PS4 dashboard in order to install the update. Microsoft has confirmed that publishers can choose to allow Xbox One users to download patches while playing games.
Sony also noted that "depending on the game, you not be able to access online features until all the update data is installed."