On regular TV's, the luminance channel (brightness basically... if you were to plug just a certain one of the component inputs in, you would get just a B&W picture) is sent separately from two different color difference channels. Thus, compared to a normal composite (where all 3 channels are mixed and compressed, leaving the TV to decode this) and S-video (where just the luminance is separate from one mixed color channel, basically better than composite), the composite allows for higher picture fidelity because it can offer 3 times the bandwith of composite, and without channel cross-interference... thus, superior picture.

You can get even higher picture quality (in terms of picture resolution) over component if your display systems support it. For example, the only way to display EDTV (480p) and HDTV (720p and 1080i) is over these cables. But that's another discussion altogether