A shuddering or vibration in the brake pedal when applying the brake, may be a first indicator of the need for some minor auto repair. The shuddering could be caused by a number of things, brake pads that aren’t parallel, out of shape rotors, warped drums, etc.
In a disc brake system, if the brake pads are not parallel to the rotor, they will make irregular contact and cause a shuddering as they come into and out of contact with the rotor. You will be able to feel this through the brake pedal and possibly elsewhere in the car when applying the brake pedal. When brake pads are not parallel and produce this vibration, they should be serviced immediately to avoid warping of the rotor and the need for more extensive auto repair.
A warped rotor will produce similar effects; in this case, even if the brake pads are parallel, the misshapen rotor will come into irregular contact and cause the shuddering. You can check to see if your rotors are warped by looking for extremely smooth or discolored areas on their surfaces. This will indicate that the rotor is likely already warped. Sometimes, auto repair, rather than part replacement, is an option. A warped rotor can sometimes be mechanically smoothed out and made even, though once the rotor has warped, it is much more likely to become so again. Complete part replacement is often advised.
Warped brake drums (in a drum brake system) can be another cause of shuddering in the brake pedal, though they are rarely the culprit and almost always only when mistreated. If the driver engages the parking brake too quickly before letting the brake cool down, the pressure can warp the drum, requiring possibly quite expensive auto repair.