In one of David's first memories, he recalls reading to Peggotty from a book about crocodiles. In the middle of this fascinating subject, David suddenly turns the discussion to marriage, asking if Peggotty ever plans to get married. Peggotty, who is an adult and realizes what Mr. Murdstone's presence in David's mother's life really means for David, starts looking very odd. Peggotty wonders why David is suddenly worrying about marriage. Peggotty decides to change the subject, turning David back to his crocodiles.
Just before Mrs. Copperfield marries Mr. Murdstone, David is sitting with his crocodile book when Peggotty asks if David wants to go on his first trip to Yarmouth. David's happy early memories of being taught to read at home involve the crocodile book. When David comes home for the holidays before his mother passes away, he remembers reading to Peggotty from the crocodile book, "in remembrance of old times" (8.96). When David is grown up and he goes to visit Peggotty in Yarmouth, he finds the crocodile book sitting on a table for him. And finally, in the last chapter, as David surveys his happy family, he sees Peggotty reading to David's own children from the crocodile book.
In other words, David's crocodile book, his first real book, symbolizes all the warmth and security that Peggotty brought to his early childhood. It also represents her unchanging personal loyalty to David over the years, until she is now trusted with looking after David's kids. The crocodile book is like the opposite of the "Take care of him. He bites" sign: it represents closeness to other people and family contentment.