Answer:
In active euthanasia a person directly and deliberately causes the patient's death. In passive euthanasia they don't directly take the patient's life, they just allow them to die.
This is a morally unsatisfactory distinction, since even though a person doesn't 'actively kill' the patient, they are aware that the result of their inaction will be the death of the patient.
Active euthanasia is when death is brought about by an act - for example when a person is killed by being given an overdose of pain-killers.
Passive euthanasia is when death is brought about by an omission - i.e. when someone lets the person die. This can be by withdrawing or withholding treatment:
Withdrawing treatment: for example, switching off a machine that is keeping a person alive, so that they die of their disease.
Withholding treatment: for example, not carrying out surgery that will extend life for a short time.