Due to how Sony has chosen to handle game updates on the PS4, it requires you to have enough free space on your hard drive to duplicate the game files. The system will download the update itself, which is only a few GBs, and will then start copying your entire existing game install. As the system copies the full game files, it checks for corrupted data, and applies the updated files. Once the full file has been copied, and checked for errors, then the duplicate file is removed.
Unfortunately, this method of updating can be problematic for users tight on hard drive space, or internet bandwidth. Until Sony decides to change how they handle updates for the PS4, there is not much to be done. Interestingly, they do not use this update method for the PS5.