Go into the wii menu, select the wii icon on the bottom of the screen... go to the wii settings menu, not the data save menu.
Find the "internet something or other" button, I think you have to hit the next scroll button at least once. Don't go to the wiiconnect24 settings button.
somewhere in there you will find your wii mac address..
sorry if this sounds like a zelda walkthrough, Im sure you get the drift of where to find it...
Oh, and a MAC address is just like a unique identifier for your wii console... Sorta, not really, like how you access a computer or website through their ip address...
Its just a way for you to let your wii have access to the network by allowing this MAC address, if that is what you are doing??
(Im using sygate firewall and have as yet had no luck just saying "allow all" from my wii via its MAC.)