Hello, how does the option to approve login requests work?

Approve session start requests
use this device to approve login requests made from other devices

How does it work?

Thanks

I assume you are referring to the Log in with Device feature and not 2 Factor Authentication. If so, you can find information here:

Please let me know if you have any additional questions.

Is there a backup if you lose your device? Or what happens then?

You can always log in using your master password. For the Web Vault, you can also use a passkey to log in.