Allusion in Macbeth

Hecate is a Greek goddess who presides over magical rites and is associated with witchcraft, the night, and the underworld. Her mention here in Macbeth's soliloquy is important considering later developments in the story with the three witches.

In Roman mythology, Neptune is the god of the sea. Macbeth invokes this name to emphasize his belief that all the water in the world will not be enough to wash the blood (guilt) from his hands.

Macbeth realizes that nothing will clean (wash) the blood from his hands. Now that he has murdered, his hands will always be covered with blood (figuratively), and he will never be free of guilt. This is also an allusion to Pontius Pilate and his washing of his hands (stating that he was innocent of Jesus' blood which was spilled during his crucifixion). 

Macduff compares the murder of Duncan to a picture of Judgment Day ("the great doom's image"). He calls everyone in the castle to rise up—as the dead would on Judgment Day—to witness the horror. Note how his speech is broken and truncated in this passage to emphasize his extremely agitated state.

In Greek mythology, Gorgons were monsters who could turn anyone who looked at them into stone. The most famous gorgon was Medusa. Macduff uses this phrase to say that the sight of the murdered king is as terrible and destructive as seeing a Gorgon would be.

Macbeth asks the murders whether they are so indoctrinated with the lessons from the New Testament that they would not carry out the deed. The lesson he is referring to is one in which Jesus advises that people love and forgive their enemies.

Shakespeare learned the story of Antony and Caesar them from Plutarch's Lives, which he had read a few years before writing Julius Caesar. Macbeth's allusion to these characters represents how Caesar's genius, or spirit, overpowered Antony's even though Antony was a better man in many respects.

Acheron is one of the rivers in Hades according to classical Greek mythology. Since it is associated with the underworld, then it has connections to the Christian concept of hell, evil, and the devil. The witches have been portrayed as associated with the devil, so Hecate suggesting they all meet at "the pit of Acheron" reinforces this notion that they are wholly evil.

Macbeth's exclamation alludes to a belief during the reign of James I of England (the Jacobean era) that a thunderclap ("crack") announced the coming of Doomsday ("doom). Essentially, Macbeth thinks that Banquo's children and heirs will reign for a very long time.

This word represents a non-standard spelling of "harpy." In Greek and Roman mythology, harpies are horrifying monsters that have women's faces and the bodies of birds. They are regarded as filthy and covetous, always preying on others and wanting more. While they sometimes supposedly administer divine vengeance, commonly their mention or presence contributes to a dangerous or evil atmosphere or theme, as in this case with the witches.

Evidently Macbeth is referring to Brutus who chose to commit suicide by having a soldier hold his sword pointed at him and running onto it rather than surrender at the battle of Philippi. Macbeth would know about it from reading Plutarch. Shakespeare drew from Plutarch to dramatize the incident in Julius Caesar.