The hard drive can be removed and a larger drive installed. Once a larger drive is installed when booting the PS4 it will initialize the drive and claim it for PS4 use. When connecting to the PlayStation Store you can re-download games that you purchased through the store .... Might Take a While as for games can be quite large. Save the 500GB drive to the side in case larger drive ever dies or format it and use it in a laptop or some other application where you have a need for 500GB storage.
I have been told that the hard drive replacement/upgrade process is the same for the PS4 as it is for the PS3 in that it will recognize a bare drive and it will create the partition and the handshake to the replacement or larger drive.
I have done this process for a PS3 and with the PS3 its a very simple swap. And actually the PS3 I got for free because the Hard Drive was crashed. I pulled a 40GB SATA HDD from an old laptop and put that into it and was back up and running in less than a half hour. Once connected to PlaySation store I was able to download games to the 40GB SATA HDD. So I have Minecraft, Diablo 3, and Little Big Planet 1, 2 and 3 and Hamster Ball on it for my daughter, in which I play Diablo 3 on it occasionally, but prefer it more on PC for controls etc.