The Wii Component Video Cable lets you connect your Wii to a high-definition TV (HDTV) or to an enhanced-definition TV (EDTV) so you can enjoy 480p (progressive or non-interlaced video output) instead of the usual 480i (interlaced display) screen resolution.

What is 480p? What is 480i?
The "p" stands for progressive scan - that means that the TV or monitor draws each frame you see in your screen line-by-line from top to bottom - of course this (usually) happens so fast that your eye sees one instant image. The opposite of progressive scan is "i" - that means interlaced - the monitor or TV draws every other line in your screen, and then, it goes back to the top and draws the remaining lines (like tying knots in a lace).

Interlaced scanning is a bit of a cheat. It makes your frames look like they're drawing faster (because you have every other line drawn from top to bottom in half the time - and it fools your eye into seeing one whole image), but the problem is that it can flicker. "Everybody" knows that "p" means a higher-quality image than "i" because a screen that does 720 lines from top to bottom one-after-another will look better (you have a pure solid image) than a screen that does every other line (it does 360 lines and goes back and does the other 360).

The number before the "p" or "i" stands of for the number of lines drawn on your screen, so 480p and 480i both make 480 lines on your screen. If it was 720 or 1080, then there would be more lines. The more lines you have, the better your resolution. But if your TV sucks anyway or if you're the type of person who can't notice a difference, then it doesn't really do you any good to invest in all this "p" stuff.

Do I need the Wii Component Video Cable to enjoy 480p?
No other kind of cable will let you enjoy progressive display. That is, no other kind of cable you can buy. But you can make your own set-up because you can easily find out the pinout. The good folks over at the nfg.forums have been discussing the pinout for days now.

A pinout is a description of how a connector (like a USB or video cable) is wired - in other words, a pinout lets you know the purpose of each shiny metal "tooth" or "pin" sticking out of the connector cable. And it lets you make your own. Below left, you have the connector cable (picture taken by RGB32E from the nfg.forum). In the middle is the pinout at nfggames' wiki. To the right you have acem77's creative setup.