As generally understood, the person accusing (the "pot") is understood to share some quality with the target of their accusation (the "kettle"). The pot is mocking the kettle for a little soot when the pot itself is thoroughly covered in the same.
An alternative interpretation, recognised by some, but not all, sources is that the pot is sooty (being placed on a fire), while the kettle is clean and shiny (being placed on coals only), and hence when the pot accuses the kettle of being black, it is the pot’s own sooty reflection that it sees: the pot accuses the kettle of a fault that only the pot has, rather than one that they share. This is also an outdated statement, since most pots & kettles are of metallic or ceramic materials. (See also: Psychological Projection)
The following poem can be found in the schoolbook Maxwell's Elementary Grammar from 1904.
"Oho!" said the pot to the kettle; "You are dirty and ugly and black! Sure no one would think you were metal, Except when you're given a crack."
"Not so! not so!" kettle said to the pot; "'Tis your own dirty image you see; For I am so clean – without blemish or blot – That your blackness is mirrored in me."
In Ancient Greece, mention of ‘the Snake and the Crab’ signified much the same idiom. The first instance of this is in a drinking song (scholium) dating from the late 6th or early 5th century BCE. The fable ascribed to Aesop under this name makes the crab an honest actor who kills the snake for the common good. In another, however, concerning a mother crab and its young, the mother tells the child to walk straight and is asked in return to demonstrate how that is done.
A similar story 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 the Gospel of Matthew 7:3, Jesus is quoted as saying, during the discourse on judgmentalism in 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?" Many scholars have interpreted this as a proscription against personal attacks in general, not just particulars.
A widespread European proverb (see below) whose English equivalent is 'those that live in glass houses should not throw stones' also counsels caution from being judgmental. It appears in the work of Geoffrey Chaucer as 'One who has a glass head should beware of stones' (Troilus and Criseyde II/867-8) and in George Herbert's Outlandish Proverbs (1640) as 'Whose house is of glasse, must not throw stones at another' (#196).
In Mexico, the phrase goes "el comal le dijo a la olla...", literally the "comal" said to the pot. Although the full phrase goes "el comal le dijo a la olla, que tiznada estas" (‘the comal said to the pot, you are so full of soot’), for most people it is reminiscent of a popular children's song by Francisco Gabilondo Soler "Cri-Cri" in which the comal complains to the pot for laying on top of it (‘el comal, le dijo a la olla, oye olla, oye oye!, si tu te has creido que yo soy recargadera’). Hence, when asking people in Mexico to complete the phrase, most would answer "oye, oye".
The 4th-century BCE Chinese philosopher Mencius relates a similar story about a soldier deserting a battleground who mocks another soldier for having fled farther than he has: 'He who has retreated fifty paces ridicules another who has taken a hundred' (五十笑百 wushi xiao bai).
In the Lithuanian language, a similar proverb exists: juokiasi puodas, kad katilas juodas (lit: "the pot laughs that the cauldron is black").