Checkout means a single user has control of the map. They have checked the map out to their device and no one else can edit the map on Mindjet Files. When a mobile device opens a map on Mindjet Files it automatically checks the map out.
The implications are that if anyone else opens the map and edits it, their changes will not be saved. You can edit a copy and save it but its not fun trying to merge the maps later. Wait for the map to be checked in. Treat a checked out map as a view only map.