Hecate appears in Act III, Scene V (there seems to be a mistake in the enotes linking of the text - and it's suggesting, incorrectly, that Hecate appears in Act V, Scene V). She arrives, looking angerly, and makes an angry speech to her fellow witches:
How did you dare
To trade and traffic with Macbeth
In riddles and affairs of death;(5)
And I, the mistress of your charms,
The close contriver of all harms,
Was never call'd to bear my part,
Or show the glory of our art?
Traditionally the queen of the witches, Hecate seems to want to be more involved in the witches' manipulation of Macbeth. Hecate later makes a rather spurious appearance in Act 4, Scene 1, and is mentioned by Macbeth in his soliloquy Act 3, Scene 2.
But - and this is the key point - most scholars believe that Hecate and her scenes are NOT written by Shakespeare, and were later added to the play by another playwright (probably Thomas Middleton, who wrote another play entitled "The Witch"). So they're not usually written about or considered as part of "Macbeth".
Hecate is the Greek goddess of the witches and she is mad with the witches because they the other witches did not even invite her in making mischiefwith them. Because she is the Queen of darkness and witches she would like to do mischief and mess with people.
but( to the other person who answered this question ) in the book we have read at school Hecate comes in in Act 5, but i am not sure!! could you explain to me a bit better who Hecate is why is she mad with the witches, why does she want to see macbeths downfall and what are her purposes and why does she exist and what does she want people to think about her! its because i am doing homework and i have to write a diary entry as if i am her answering all these questions! thanks