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.
Socrates
Socrates lived during the time of the transition from the height of the Athenian hegemony to its decline with the defeat by Sparta and its allies in the Peloponnesian War. At a time when Athens sought to stabilize and recover from its defeat, the Athenian public may have been entertaining doubts about democracy as an efficient form of government. Socrates appears to have been a critic of democracy, and some scholars interpret his trial as an expression of political infighting.