What is a System Code? Why do I have one? What can I use it for?
Much like Friend Codes on the Nintendo DS, a System Code is a unique number for your Wii system. In essence, it is your Wii's address/phone number/IP address/ID number. You use it to identify your system to others. This is important because online games will have "Friend Code" options where you can choose who you want to play, but you must have first exchanged a System Code with them. Note: It remains to be seen if you will be able to directly pick opponents, even in the Friends option - the Nintendo DS does not really allow this, and there is speculation that the Wii will be handled in the same way, despite being mostly unpopular.
eldad9 clarifies that: "It identifies the device; so it's not like a phone number, but a International Mobile Subscriber Identity (the mobile phone ID in the SIM card); not like an IP address (which can change) but a MAC address (which is constant)."