A car shaking as you brake (aka pulsation) usually indicates a problem with brake rotors.
What is a brake rotor? When you depress the brake pedal, your vehicle’s master cylinder sends brake fluid into the brake lines and calipers. These calipers are lined with brake pads and encircle your brake rotors. Brake pads squeeze the surface of the rotors, which slows the vehicle and prevents the wheel from turning.
Rotors are exposed metal and often become warped or rusted. This happens most often when a car is left unused for extended periods of time. While driving, the friction of use will generally keep the rotors clean.
If your car has been sitting for a short while, sometimes driving the vehicle will clean off the rotors. However, if you experience pulsation, it is important to have it checked by a technician. Your technician will pull the wheels off, measure for wear, and check for corrosion. Worn rotors are not necessarily dangerous, but you should still have your vehicle checked to confirm the diagnosis.