We first meet Madame Therese Defarge the wife of the wine shop owner Ernest Defarge in Ch.5 of the First Book of "A Tale of Two Cities." Dickens describes her commanding presence in the following manner:
Madame Defarge, his wife, sat in the shop behind the counter as he came in. Madame Defarge was a stout woman of about his own age, with a watchful eye that seldom seemed to look at anything, a large hand heavily ringed, a steady face, strong features, and great composure of manner. There was a character about Madame Defarge, from which one might have predicated that she did not often make mistakes against herself in any of the reckonings over which she presided. Madame Defarge being sensitive to cold, was wrapped in fur, and had a quantity of bright shawl twined about her head, though not to the concealment of her large earrings. Her knitting was before her, but she had laid it down to pick her teeth with a toothpick.
Initially Madame Defarge's act of knitting seems innocuous and inconsequential, but much later in Ch.15 of the Second Book which is appropriately entitled "Knitting," we come to know the real reason and the sinister purpose of her knitting:
`Jacques,' returned Defarge, drawing himself up, `if madame my wife undertook to keep the register in her memory alone, she would not lose a word of it--not a syllable of it. Knitted, in her own stitches and her own symbols, it will always be as plain to her as the sun. Confide in Madame Defarge. It would be easier for the weakest poltroon that lives, to erase himself from existence, than to erase one letter of his name or crimes from the knitted register of Madame Defarge.'
This chapter deals with the road mender's account of the hanging of Gaspard which in turn incites the revolutionaries to violent action. The Evremonde family which has hanged Gaspard is doomed for destruction because Madame Defarge has knitted their names in a secret code to be always remembered by her.
It is only then we realise that Madame Defarge has been throughout the entire novel painstakingly knitting all the names of the aristocrats who are to be killed by the revolutionaries. She uses her own set of symbols and codes to disguise her sinister intentions. Her knitting thus serves as a mnemonic device - a "register" - to aid her thirst for revenge.