the physics of it in a nutshell is this: when you countersteer, and lean as you normally would, you end up bringing the contact patch on the front whell closer to you, thus shortening your wheelbase, making for a smaller turning radius.

In a car this is done to force the car to move laterally instead of in a spiral pattern (
(spin).

As far as how to tighten corners in a car...that varies on what drive configuration it has....bikes are at the least far simpler in that perspective