What is the S-Video cable for ?

The S-video interface was introduced back in the late 1980's as a more compact and lower loss way to interface video signals between video components. Prior to that the most common way to connect video components was through coax cable with the screw-on F-type connectors (like the cable company still uses) or "RCA"-style plugs. In the 90's it was quite common for components such as TVs, VCRs, DVDs etc to offer S-video as a connection method. But later on component video became more common - using separate cables for the red, green, and blue components of the video picture. Today the digital HDMI interface is the most common. You can still use S-video to hook up your equipment, but HDMI or component video will typically provide a better picture.

But later on component video became more common - using separate cables for the red, green, and blue components of the video picture

You're somewhat correct on that. The three separate parts of the component or YPbPr cables, are red and blue, but also luminance (not green).

Everything else is correct.