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This short video shows how to use your cPanel (that is the hosting control panel) to backup your WordPress installation and database, etc. That is what the 'warning' before you do an autoupgrade is referring to, but my nightly backups preclude the need to for the most part, but if you are safety conscious, I wouldn't ever discourage doing this. And while a WordPress upgrade should not harm your site–and IS RARE, many times unsupported/un-updated plugins or even badly coded themes can break your site. At that time a roll back to your last backup is necessary.
While I do back up your site (those hosted by me),* you may wish to keep a snapshot of your installation on a monthly or weekly basis (as I only go back one week and one monthly snapshot) that you can keep on your computer if you ever want it. I encourage you to do a manual backup before doing anything major. I can roll back your site to the latest version, however if backups for the night before are still running, I will have to use the last complete backup (you may lose one day). You can make as many backups as you'd like, however all I ask is that you only keep the latest one on my server… download and delete the other versions (I show you how at the end of this video.
*Clarification of automated backups by WebsByAmy: a benefit of my hosting is daily backups (but they backup the day before, overwriting the day before that) as well as weekly (that overwrite the previous week) and monthly (overwriting the prior month's). However, you can make backups in a matter of minutes–and it includes all aspects of your hosting (your email, databases, etc.) in a manner that is easily (by me) restored.