The two convicts Pip encounters are Abel Magwitch and his partner, the evil gentleman conman Compeyson. When Pip first meets them, he is a small boy. He is visiting his family tombstones in the graveyard on the marshes and encounters Magwitch, a fearsome but generally kind-hearted convict. Magwitch is on the run, but also chasing. He tells Pip he has a partner, way more ferocious than he is.
Now, I ain't alone, as you may think I am. There's a young man hid with me, in comparison with which young man I am a Angel. That young man hears the words I speak. That young man has a secret way pecooliar to himself, of getting at a boy, and at his heart, and at his liver. (Ch. 1)
In reality, there is no “young man.” Magwitch is trying to scare Pip into compliance. He doesn’t really have the heart to threaten too harshly himself. He is not alone, however. Compeyson is also on the run, and Magwitch is looking for him. He blames Compeyson for his arrest and the fact that he is being deported to Australia.
Pip does encounter Compeyson, and when he tells Magwitch that there is someone else on the marshes dressed like a convict, Magwitch goes ballistic. He wants to find and kill Compeyson. What he does succeed in doing is getting both of them captured.
Magwitch had Pip steal some food for him, and a file to remove his shackles. When he and Compeyson are caught, Magwitch does something interesting. He tells the police that he is the one who stole from the blacksmith, so that Pip will not get into trouble. Pip is grateful, but he has no idea what an influence Magwitch will have on his life.
Magwitch goes to Australia and makes his fortune. He arranges with Jaggers to have it doled out to Pip, keeping his identity a secret. Pip assumes that the money comes from the only rich person he knows, Miss Havisham. They share the same lawyer, and many of the same circle, so it is not much of a stretch. She does nothing to correct Pip in thinking this.
One day, after Pip has been living off of Magwitch’s money for a while and is dressing, talking, and acting like a gentleman in London, Magwitch shows up and tells Pip who he is. Pip is appalled. All of his hopes and dreams go up in smoke. Magwitch terrifies and disgusts him. Magwitch turned Pip into a gentleman, but his own habits are quite coarse.
Magwitch explains that Pip did him a kindness he never forgot. Pip feels like he turned his back on his family for nothing.
Miss Havisham's intentions towards me, all a mere dream; Estella not designed for me ... But, sharpest and deepest pain of all—it was for the convict, guilty of I knew not what crimes, and liable to be taken out of those rooms where I sat thinking, and hanged at the Old Bailey door, that I had deserted Joe. (Ch. 39)
It gets even worse. Magwitch is in danger. If Compeyson or any of his old criminal associates find out Magwitch is in London, he will be arrested and hanged. Wemmick, Jaggers’ assistant, and Jaggers, attempt to guide Pip without incriminating themselves. They tell him to get as much of Magwitch’s property in his own name as he can. Pip doesn’t. He tries to flee with Magwitch. Compeyson finds them when they are in the river trying to escape. He is killed, and Magwitch is hurt badly.
Magwitch dies in prison before he can be hanged. Penniless and in debt, Pip is thrown into debtor’s prison. He didn’t get Magwitch’s portable property, and it went to the state. Pip returns to a more humble life after Joe bails him out.
Compeyson's influnce on Pip was not just Magwitch's association. In an interesting twist, Compeyson was also the man who jilted Miss Havisham. Thus, Compeyson had almost as much of an influence on Pip's life as Magwitch did. Magwitch was also Estella's father, so his life and Magwitch's were intertwined from the time he was a small boy.