For the first option, Do not download or install means that you will not be given ANY updates at all and your forum will remain at the same version the entire time.
I'd say this is useful for people who don't want to mess around with forum settings, install manual mods (which aren't recommended) or would like better optimisation (if they need it for example). You can still download updates and manually place them in the folder include/updates if you'd like to install certain updates.
The second option, Install pre-downloaded updates only will automatically install any updates you have manually uploaded to the folder include/updates to your forum. An update cache is generated on first page load and after this uses a background task to regenerate periodically when you choose, or you can disable the task entirely if you don't want it to re-generate.
Once it runs, if it detects you have placed an update in the folder it will automatically install it for you.
The third option, Download but manually install downloads any available updates from the Panther website when the background task runs but leaves them in the folder include/updates and also puts out a notification on the Admin panel notifying you that a new version is available. You'll also see a new link at th ebotto of the admin menu entitled 'Forum updates'.
On this page you can manually review and install the update available for your forum.
Finally, Download and install downloads and installs any available updates automatically through the background task which is ran.
chris [at] get-aura [dot] org