Why won’t it work when I turn my phone off like it supposed to?

Plug it in when on your home WiFi network, and simple lock the display (press the power button once). It will then backup.

As nny1001 already mentioned, if you power it off, it is inert and cannot access the internet to backup.

See -> How to back up your iPhone, iPad, and iPod touch with iCloud - Apple Support

Your phone shouldn't be powered off entirely. In order to back up it has to be on wifi.. charging... and in a standby state. If you power it off, it doesn't do anything but hold papers down on your desk.