What does it mean when your car shakes wen you brake?

It's not so much the "car shaking" as it is feedback through your foot from the brake hydraulic system. YOU are shaking -- at least your foot is -- and you're assuming that it's the car.

Most likely, your car is equipped with disc brakes on the front, possibly on the rear also. Disc brake rotors warp. It usually happens due to overheating, but it can be the result of a manufacturing defect. The "thumping" effect is a real attention-getter!