Access the PS4 Safe Mode
In this thread, you'll learn how to access the safe mode function on the Playstation 4, which is very simple.
Usually, the safe mode activates when your console does not power down properly or when replacing the PS4's hard drive. It can also appear when unplugging the PS4 when the system is still running (which we strongly advise you NOT to do!)
To simply access the Safe Mode, hold down the power button for at least 7-8 seconds. After that, the safe mode display will come up on the screen which should look like this:
1. Restart System - Ends Safe Mode and restarts the PlayStation 4 normally.
2. Change Resolution - Changes the screen resolution to 480p when the PlayStation 4 is restarted.
3. Update System Software - Allows the PlayStation 4 to update the system software via Internet, USB Drive, or Disc.
4. Restore Default Settings - Restores the PlayStation 4 to the default factory settings.
5. Rebuild Database - Scans the drive and creates a new database of all content. This operation may take a long time depending on the type and number of data items.
6. Initialize PS4 - IMPORTANT: All data and settings will be lost by performing this step.
Deletes all user data and restores the PS4 to as if it just came out of the box. This option is the same as [Initialize PS4 ] in the (Settings) menu. System software (firmware) is not deleted.
7. Initialize PS4 (Reinstall System Software) - IMPORTANT: Deletes all information on the HDD, including the System Software. A message that states a USB storage device containing the System Software must be connected, is displayed. Then you can confirm the selection.
Source: PlayStation Support
For a visual guide, refer to this video: