To back up your PS4 data online, you need a PlayStation Plus subscription. While logged in to your PlayStation 4 with the same account you use with PlayStation Plus:
Choose Settings from PS4’s home menu. Then, Application Saved Data Management, proceeding to Saved Data in System Storage.
Select Upload to Online Storage and then the data you want to back up to PSN. Finally, choose Upload on the right. Answer positively if your local saves are newer than any online saves, and you don’t mind overwriting them.