It is interesting to note that many critics suggest that this scene with Hecate was not written by Shakespeare in the original play or even was perhaps added in later by some other playwright to give the audience more of the supernatural they often crave.
Hecate is the "head" witch so to speak and in her speech she is full of ire for the other witches for not letting her in on the fun with Macbeth. It is her decision to give him false hope with the apparitions and lull him into a sense of security which will be his ultimate undoing.
Hecate appears in Act III, because she is angry with them for wasting their efforts on someone like Macbeth. She feels that they have not used enough mischief with Macbeth and also, the fact that Macbeth has not been grateful to the witches for what they have given him. She feels that he is ungrateful and selfish. Hecate, therefore, decides to take charge of Macbeth's fate. She will conjure up more chaos, and greater turmoil for Macbeth.
Hecate's purpose is to make Macbeth feel over confident, she says that over confidence is man's worst enemy. Therefore, the second prophecy that is given to Macbeth holds two very important exceptions, which he does not figure out until it is too late to change his actions.
Hecate sets up Macbeth for his ultimate undoing. It is Hecate's purpose to unleash more evil into the world to create more suffering.