These lines from Macbeth, often regarded as a subtle tribute to King James I, are spoken by a doctor arriving at the palace in advance of King Edward the Confessor, interrupting a dialogue between Macduff and Malcolm. When they ask for the king, the doctor explains that he has stopped to heal those suffering from scrofula, which is here described as the "malady" that is later called "the evil." "Such sanctity hath heaven given his hand—They presently amend" refers to the prevailing belief that the Christian God had conferred the divine power to heal on royalty.

In the context of the play, the lines refer to the need for a regent with the requisite virtue to heal a country now ruled by a maddened, bloodthirsty regicide. These lines complement Malcolm's just-spoken description of the fundamental moral soundness of his character and capacity to rule, and they also provide a glaring contrast with the growing depravity of Macbeth, as is soon revealed by the slaughter of Macduff's wife and children.

It was an interesting tradition or belief that the King's touch was able to cure scrofula, which was a disease at the time. Note how this passage is set in a scene that very much compares and constrasts the King of England with Macbeth, who is now the King of Scotland. Of course, the goodness and the way that the King of England is divinely appointed to his role is emphasised, compared to Macbeth, who has seized the crown. The number of omens and supernatural events that occur obviously indicate that this was an unnatural event that has gone against nature.

However, the words of the doctor in the quote you have highlighted refer to the King of England and his goodness in using his divine power to cure the sick. He says that their sickness necessitates the greatest effort of medical skill, however the divine power that God has given him cures their illness at his touch.