What is the purpose of the description of the concoction the witches make in Act IV, scene 1 of "Macbeth"?
The description of the witches' concoction is simply two-fold. First, it serves to define them as witches who perform the black arts. Secondly, it is Shakespeare's usage of actual historical information. When King James I became King of England, he was opposed by certain groups of people. Agnes Seaton and a group of women were among these groups of people who did not want a Scottish king leading England. Originally, they had hoped to poison the King using his own clothing, but they could not find a way to get their hands on his attire. So, they had to resort to curses. In their testimony, they claim to have created a concoction very similar to that of Macbeth's witches in the hope of cursing King James. Part of their curse was to create adverse weather conditions which would sink his ships. As luck would have it, however, a terrible storm did actually occur and destroyed a ship carrying James' wife's gifts from abroad. Rather unfortunate for both the Queen and Agnes Seaton, for Agnes was tried and convicted of witchcraft as a result. Shakespeare uses this information to not only create vivid characters in his play, but to compliment James by using the King's life to inspire his work.
The witches are being clearly established as practioners of the black arts in this scene. Even though we've already seen them do other acts typically identified with witches such as in Act 1, scene 1, when they chant and respond to their cohorts, Graymalkin and Paddock, and then in Act 1, scene 3, when they seem to disappear, by having them concoct this disagreeable potion in 4.1, they are even more firmly identified as witches. Also, they are preparing to conjure up visions for Macbeth to see--visions that will purposely lead him astray. They plan to bring him down completely, which is a very heinous act. Therefore it is fitting that the contents of this potion be some of the most disgusting ingredients possible. Many of the ingredients suggest violence ("Liver of blaspheming Jew,/.../Nose of Turk and Tartar's lips"), and Macbeth is a man of violence.
Third Witch: ...Liver of blaspheming Jew,/Gall of goat, and slips of yew/Silver'd in the moon's eclipse,/Nose of Turk and Tartar's lips,... (4.1)