What exactly the Camera RAW Calibration tool does?

I'll add, there is no reason you can't, if you desire and can get a visual result you desire, use the Calibration Pane to edit the image. But as outlined, originally it was used for a different purpose prior the ability to build and edit your own DCP camera profiles. 

Before Adobe Camera Raw had camera profiles, the Calibration panel was used for customizing how Camera Raw interpreted the raw data into RGB colors. The Calibration panel isn’t needed as much for that now, so today the Calibration panel is used more for creative color manipulation on top of the currently selected camera profile.

The Calibration controls do affect color in a different way than Temperature/Tint or HSL, which is why they’re still useful. You can watch a good demonstration of the differences by Blake Rudis of f64 Academy on YouTube:

I set the video link to start at 7:45, but of course you can also watch the video from the beginning if you want.