The cause of pulsation and vibration is most commonly warped brake rotors. When the brakes are applied, the brake calipers press the brake pads against the rotors that rotate with the wheel. If the rotor is warped so the surfaces are not parallel, the caliper pistons are rapidly pushed in and out as the pads contact high and low spots. These pulsations will cause the entire wheel to vibrate.
There are several causes for warped rotors. It can result from normal wearing of the rotors. It will often occur if you let the brake pads wear to the point where is there is metal-to-metal contact between pads, or what's left of them, and the rotor. Thus, the importance of routine brake pad inspections.
The amount the rotor wobbles is called the run-out. In some models pulsating will occur at just 0.001 inch, but other manufacturers allow run-out up to 0.003 inch. Determining run-out requires special equipment. If there is not too much run-out the rotors can be repaired by precision shaving away some of the rotor to make the surface smooth and even. If the run-out is too high then the rotor will need to be replaced.