Answer:
The convict, Abel Magwitch, was actually Estella's father, but Pip doesn't find out until the end. Only Jaggers, Herbert, (possibly Wemmick) and Molly knew this. Jaggers had solved a case regarding that Molly had murdered another woman (complicated relationship between Magwitch, Molly and another woman) and was about to kill the baby Estella when Magwitch put her into Jaggers' care (then gave her to Miss Havisham).