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Component vs. Composite
Component cables are high-definition compatible cables that split a video signal into three separate parts, or components. This is different than traditional composite video cables, which transmit the entirety of a video signal over one cable. Composite cables cannot handle the bandwidth required to transmit high-definition video, so they can not display HD signals.
Incompatibility
The original PlayStation was released in 1995, and while the PS One is a slimmed down version of that system, it basically employs the same technology. The hardware inside the PS One was designed for either composite video cables or coaxial video. Even though the component cable designed for the PS2 and PS3 will fit on the PS One's video port, it will not properly display the game's graphics.
Significance
Not only is the PS One incompatible with component video, but the games made for it are as well. The PS2 is backwards compatible with PS One games, but if the PlayStation is connected to a television using component cables, PS One games played on it will not display properly.