Information from the F-Droid Site:
This is for an app called System App Mover, but it's description is correct.
System apps can get more privileges, so some apps get more
functionality when installed as a system app.
On the other hand, system apps can not be uninstalled. So this app can
also be used to convert system apps to normal user apps by moving them
from the /system/app directory to /data/app directory.
WARNING: Uninstalling important system apps might result in a unusable
device! Use this function at your own risk and only if you know what
See What do android application permissions mean. There are some permissions that have a "level" of "system". Those can only be used by applications that are "system" applications. I do not know why f-droid would need them. Maybe the INSTALL_PACKAGES permission. This would allow f-driod to install an application, like Google Play does, instead of sending the Install request off to the Package Manager application.