Brain death is the complete loss of brain function (including involuntary activity necessary to sustain life). It differs from persistent vegetative state, in which the person is alive and some autonomic functions remain. It is also distinct from an ordinary coma, whether induced medically or caused by injury and/or illness, even if it is very deep, as long as some brain and bodily activity and function remain; and it is also not the same as the condition known as locked-in syndrome.
No, it is not allowed to take off the ventilator, because that can lead to stopping the person from breathing and cause his death. We must keep on trying to keep the patient alive (breathing) as far as we can.