The SD card in the wii has a few uses.
1 - Expansion to the onboard memory so you can copy any VC games or channels onto the SD card if you are running out of on-board memory. As pointed out previously, you cannot play games/use channels directly from the card. (Hopefully Nintendo can resolve this with a software update)
2 - Store photos/music/videos for use with the photo channel. Not all file types are suggested but Nintendo has listed those that are.
3 - A method of moving saved games between Wii consoles. ie play at someone else's house and you can take your unlocked characters etc with you.
Hopefully future games will also include downloadable content which would probably be too large for the internal memory and therefore SD cards would be used for storage.