You got yourself a component cable. It has 5 cables: two for sound and three for video
you will notice that they are grouped, so the pair red and white are audio left and right, and the other three cables are, one for luminosity (green) and the other two for color (red and blue).
If you try to plug that into a TV that only supports composite video (two for audio, and a yellow one for video) the best result you can get is plugging the green cable in there and getting only the luminosity, that is the black and white part which is what you got.
That said, check if your TV supports component input, look for green/blue/red colored inputs and just plug the other two cables in.
If it does not, try to get a composite cable, for example this one seems to have decent reviews
http://www.amazon.com/9-8-S-av-Cable-Nintendo-Wii-DS/dp/B000P6L9UY/ref=sr_1_6?ie=UTF8&s=videogames&qid=1239563803&sr=1-6
and just plug the yellow cable on the yellow socket and you will have color.
Component cable gives you a better image than component, but I guess in the Wii it doesn't matter that much because it is not HD anyway.