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.
Phaedo
In order to alleviate Cebes' worry that the soul might perish at death, Socrates introduces his first argument for the immortality of the soul. This argument is often called the "Cyclical Argument". It supposes that the soul must be immortal since the living come from the dead. Socrates says: "Now if it be true that the living come from the dead, then our souls must exist in the other world, for if not, how could they have been born again?". He goes on to show, using examples of relationships, such as asleep-awake and hot-cold, that things that have opposites come to be from their opposite. One falls asleep after having been awake. And after being asleep, he awakens. Things that are hot can become cold and vice versa. Socrates then gets Cebes to conclude that the dead are generated from the living, through death, and that the living are generated from the dead, through birth. The souls of the dead must exist in some place for them to be able to return to life.