The Component cable is the most advanced connection available for the GameCube.
The cable plugs into the system's Digital AV Out port, and provides 480P Progressive Scan on compatible games. The cable also works in interlaced mode, so any non-progressive games will still work. Games, whether they are Progressive Scan compatible or not, look noticeably sharper and clearer. Colors look more vibrant. Certain details are easier to notice.
The audio plugs on either the Composite cable or S-Video cable are needed for audio, as the Component cable doesn't have audio plugs.
To enable Progressive Scan, make sure you're playing a compatible game and then press and hold the B button when turning on the GameCube. A message similar to the one in the screenshot above should appear. Select "Yes" to turn Progressive Scan on. You do not need to press the B button everytime, only when you are using Progressive Scan for the first time or you ever decide to turn it off.
To use the cable, you'll need to make sure your GameCube is the original (DOL-001) model. The Component cables can't be used with the newer DOL-101 model, as it does not have the Digital port.
Though 99% of the GameCube's games run in 480i or 480p, these two games are an exception and may not display properly or at all on an HDTV with the Component cable. While Ocarina of Time and Majora's Mask should display fine, both Zelda 1 and Zelda 2 in the Collector's Edition disc run in 240p. Turning on Progressive Scan mode should fix the problem.
Also, the majority of Mega Man X Collection runs in 240p with no Progressive Scan (480p) option. Only the Mega Man X Collection menus and the Mega Man Battle & Chase game run in 480i, while the Mega Man X games run in 240p. I suggest using the Composite cable or S-Video cable when playing this compilation. Or, if you would prefer using the Component cable, hook your GameCube to a Standard Definition TV with Component connections.