Someone being hypocritical and chastising someone else for something they themselves are guilty of.
This phrase originated in the medieval kitchen, when both pots and kettles were made from sturdy cast iron and both would get black with soot from the open fire.
Its earliest appearance is in Thomas Shelton’s 1620 translation of the Spanish novel Don Quixote. The protagonist is growing increasingly restive under the criticisms of his servant, Sancho Panza. It is identified as a proverb in the text, functioning as a retort to the person who criticizes another of the same defect that he plainly has.
It was also recorded in England soon afterwards as “The pot calls the pan burnt-arse” in John Clarke’s collection of proverbs, Paroemiologia Anglo-Latina (1639). A nearer approach to the present wording is provided by William Penn in his collection Some Fruits of Solitude in Reflections and Maxims (1682):
“If thou hast not conquer’d thy self in that which is thy own particular Weakness, thou hast no Title to Virtue, tho’ thou art free of other Men’s. For a… Drunkard to inveigh against Intemperance, is for the Pot to call the Kettle black.”
Similar themes appear in antiquity. In ancient Greece, mention of ‘the Snake and the Crab’ signified much the same idea. The fable ascribed to Aesop concerns a mother crab and its young, where the mother tells the child to walk straight and is asked in return to demonstrate how that is done.
The same theme differently expressed occurs in the Aramaic version of the story of Ahiqar, dating from about 500 BCE. ‘The bramble sent to the pomegranate tree, saying, “Wherefore the multitude of thy thorns to him that toucheth thy fruit?” The pomegranate tree answered and said to the bramble, “Thou art all thorns to him that toucheth thee”.
In Matthew 7:3-5 in the Bible, it is criticism of a less significant failing by those who are worse that is the target of the Sermon on the Mount: “Why do you look at the speck of sawdust in your brother’s eye and pay no attention to the plank in your own eye?”
The version I like best is Shakespeare in Troilus and Cressida, 1606: “The raven chides blackness.” Except, of course, a raven wouldn’t be that silly.