Damon is a close friend of Pythias, who is sentenced to death by the tyrant Dionysius. Damon offers to take Pythias' place in prison, allowing Pythias to go home and settle his affairs before his execution. Pythias is allowed to return to Syracuse to arrange his affairs, on the condition that if he does not return, Damon will be put to death in his place.
Initially, Damon is portrayed as a loyal and selfless friend, willing to sacrifice his own life to save that of his friend. However, as the deadline for Pythias' return approaches and Pythias has yet to come back, Damon begins to have doubts and fears. He starts to question whether Pythias will return and whether he has made the right decision in taking his place. Dionysius, the tyrant, also try to tempt Damon with power, wealth, and status if he would not return to prison.
The conflict that Damon faces in the myth is the struggle between his loyalty to his friend and his own self-preservation. He must weigh the potential loss of his own life against the value of his friendship with Pythias. In the end, Pythias does return, and the tyrant is convinced of their friendship and spares their lives, Damon's trust and loyalty shown to his friend is rewarded.
It is interesting to note that the story of Damon and Pythias is often used as a representation of the Greek concept of Philia (friendship) which was considered a highly valued virtue in ancient Greece.