When you copy a save game from your Wii system memory to an SD card (in "Data Management"), it encrypts it with an AES key known to all consoles (SD-key). This serves only to keep prying eyes from reading a save game file. In crypto terminology, the SD-key is a "shared secret".
Your Wii then signs the file on the SD card with its private (ECC) key. This is to prevent anyone from modifying the save file while it is on the SD card
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If I then give you a copy of my save file, your Wii can decrypt it because it knows the SD-key. However, it has no way of checking your Wii's signature, because it doesn't know my console's public key. To solve this problem, the save game also contains a copy of my Wii's public key -- the one that matches the private key it used to sign the save file. (This copy of my Wii's public key is called a 'certificate'.)