This problem in most cases is referred to as warped rotors; warped rotors can be the case. However the more common cause is thickness variation in the rotors. Thickness variation is basically something that happens over time due to the fact that the rotor does not rotate on the axle in a true manner allowing the rotor to wobble slightly as it rotates.
At one position the rotor will make slight contact with the inside brake pad and at exactly 180 degrees of rotor rotation it will make slight contact with the outside brake pad. Over time the steel on the rotor will become thinner at the locations that are making slight contact with the brake pads, thus devolving two locations on the rotor that are thinner than the rest of the rotor.
When you step on the brake the brake and you feel the vibration, it is due to constant changes to the pressure applied to the brake system while it is constantly compensating for the thinner and thicker areas of the rotor. To resolve this, the rotors will have to be resurfaced or replaced. It is always best to resurface the rotors with a quality on car brake lathe. This type of lathe will actually provide the lowest amount of lateral run out “wobble” in the rotors.
When replacing rotors, best practice is to position the rotor in the bolt pattern location that provides the least amount of wobble. This is done with a dial indicator and can be somewhat time consuming.