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
Claiming loyalty to his city, Socrates clashed with the current course of Athenian politics and society. He praised Sparta, archrival to Athens, directly and indirectly in various dialogues. One of Socrates's purported offenses to the city was his position as a social and moral critic. Rather than upholding a status quo and accepting the development of what he perceived as immorality within his region, Socrates questioned the collective notion of "might makes right" that he felt was common in Greece during this period. Plato refers to Socrates as the "gadfly" of the state (as the gadfly stings the horse into action, so Socrates stung various Athenians), insofar as he irritated some people with considerations of justice and the pursuit of goodness. His attempts to improve the Athenians's sense of justice may have been the cause of his execution.