By running the de-authorisation tool, a machine "slot" will be freed up on the online Product Authorisation server and can then be re-used by another machine.
You can de-authorise at any time, even without uninstalling Spore, and free up that machine authorisation. If you re-launch Spore on the same machine, the game will attempt to re-authorise.
If you have not reached the machine limitation, the game will authorise and the machine will be re-authorised using up one of the five available machines.
Running the Tool