What does "Keep images on device" do?
In the Dropbox settings screen, you'll find a toggle called "Keep images on device", which is disabled by default for all newly-connected accounts. This setting allows GIFwrapped to selectively download images to your device when you open or share them, freeing up disk space for other activities.
If disabled, the items will not be kept on device, unless you download or share them (items that have not been downloaded will be indicated with a cloud icon over the thumbnail). They're also made available for iOS to delete if it needs to, so if another app requires extra space, or you don't quite have enough space to update iOS itself, the files may be deleted to make room.
When this setting is enabled, GIFwrapped will automatically download and keep all images in your Library on-device. These files are kept permanently, so iOS will not delete them, and neither will GIFwrapped, unless you specifically delete the item from your Library.
Switching the setting on will initially cause GIFwrapped to attempt to download the images it's missing, which should mostly happen in the background, which means you should be able to exit the app and return later.
This setting will also affect how the "Clear Image Cache" button under "Advanced Settings" affects the library's images. Pressing this button will always delete the generated thumbnails of your images, but the actual images themselves will only be deleted if "Keep images on device" is turned off.
So remember: if you want immediate access to your library, and don't mind using up more space on your device to do so, turn "Keep images on device" on, and GIFwrapped will do it's best to stay up-to-date.
If you value disk space, and don't mind needing to re-download images when you need them, keep it turned off.