Google provides a facility for backing up certain system settings and app settings so that the data may be restored if your device has been wiped or reset.
This setting allows you to choose which Google account your backups should be associated with.
Not all backed-up data can be restored to any device: when switching to a new phone, most app settings will not be transferred, whereas other settings such as Wi-fi access points can usually be carried across.
Google's backup and restore functionality should be considered an convenience only. You should not use it as your sole backup, and you will always need to back up videos and photos you have taken.
Note: Some devices may offer backup services by other companies in addition to Google, such as a Samsung backup service offered on some Samsung devices, in which case similar settings will appear for the other services. The exact details of what is backed up and how it can be restored may differ between such services.