mod - a file that changes some values that the game loads at startup. The bad news is that you have to install or uninstall the mod to enable or disable the asymmetry - that means quitting the game and starting it again; there isn't a magic switch that you turn on and off.
Here is the download link for the Asymmetry Mod.
If that doesn't work, try here.
That little .package file has to be saved in the Spore Data folder. That's likely to be located on C:\program files\Eletronic Arts\Spore\data.
What does it do? Well, it makes the editors ignore symmetry, wich means that if you change a part or place a new one, it won't be mirrored on the other side of the creature or vehicle.
Some tips on using it:
First of all, don't go trying to make an asymmetric creature from scratch. The game is often unable to save your creature if you make asymmetric limbs. Uneven legs or arms on each side usually create issues with animation. So make a creature with the mod turned off, save it, enable the mod and edit the creature, makin minor tweaks.
To disable the mod without deleting the .package file from your data folder, just rename the extension to ".package.old".
Another cool way to use this mod is on the outfit editor. Outfits never give trouble, since they don't affect animation.
So be creative, an enjoy!