Most of the answers are in
this topic.
But in short:
Technically, I think the firmware is the low-level code which runs under the OS and co-ordinates its access to hardware. But firmware updates also seem to update some parts of the OS and apps too.
They're voluntary; the Gemini will inform you that a firmware update is available, and offer to download and install it — but there's no obligation. (You can also check manually in Settings -> About phone -> Firmware Update.)
Right now, if you have a rooted Android, it will offer the update and try to install it, but it will fail. So
don't accept it! We're expecting Planet to make the new firmware available for direct download in the next few days, so you'll be able to use the Flash Tool to apply it. There's supposed to be a way of doing that which will leave your apps and data intact, though that's not confirmed yet. And Planet say that once this next update is installed, future OTA firmware updates should work fine on rooted Android.