This damages or kills nerves in those areas. If the area of the brain affected controls movement of an arm, for example, that arm will be paralysed. One can get an effect like a stroke, with weakness affecting the arm, leg and face on one side of the body while the other side has normal power. There are many other effects besides weakness. Sometimes power is normal but balance is affected or there is tingling due to the involvement of sensory nerve supply.
Weakness can be very localised.
If only the small area of the brain which controls the face is damaged, the only effect is that one side of the face droops. However, another reason for paralysis of one side of the face could be related to the facial nerve fibres which control facial movement. The facial nerve passes through the middle ear and through a bony canal. Pressure on a nerve can cause it to be temporarily paralysed. So pressure on the facial nerve causes the whole of that side of the face to droop.