A grinding noise during a turn is typically a sign of a failing constant velocity joint on a front-wheel-drive car. The constant velocity joint provides power to the front wheels, allowing the car to turn.
A car grinding while slowing down or coming to a full stop is a sign of brake pads wearing thin. Brake pads will typically start out with a loud, squealing sound and eventually progress to a powerful grinding sound. A brake pad that has completely worn out will result in the metal plate clamping directly onto the brake disc, resulting in the discs having to be replaced along with the brake pads.