Crito
The dialogue takes place in Socrates' prison cell, where he awaits execution. He is visited before dawn by his old friend Crito, who has made arrangements to smuggle Socrates out of prison to the safety of exile. Socrates seems quite willing to await his imminent execution, and so Crito presents as many arguments as he can in order to persuade Socrates to escape. On a practical level, Socrates' death will reflect badly on his friends--people will think they did nothing to try to save him. Also, Socrates should not worry about the risk or the financial cost to his friends; these they are willing to pay, and they have also arranged to find Socrates a pleasant life in exile. On a more ethical level, Crito presents two more pressing arguments: first, if he stayed, he would be aiding his enemies in wronging him unjustly, and would thus be acting unjustly himself; and second, that he would be abandoning his sons and leaving them without a father.
Plato
The precise relationship between Plato and Socrates remains an area of contention among scholars. Plato makes it clear in his "Apology of Socrates" that he was a devoted young follower of Socrates. In that dialogue, Socrates is presented as mentioning Plato by name as one of those youths close enough to him to have been corrupted, if he were in fact guilty of corrupting the youth, and questioning why their fathers and brothers did not step forward to testify against him if he was indeed guilty of such a crime (33d–34a). Later, Plato is mentioned along with Crito, Critobolus, and Apollodorus as offering to pay a fine of 30 minas on Socrates' behalf, in lieu of the death penalty proposed by Meletus (38b). In the "Phaedo", the title character lists those who were in attendance at the prison on Socrates' last day, explaining Plato's absence by saying, "Plato was ill". ("Phaedo" 59b)