How is Aegeus scene relate to the overall theme of Medea?

The Aegeus scene is important to the theme of the play in several ways. On the first level, it is central to the plot: it givies Medea a place of refuge which facilitates her escape from Corinth.
Next, it shows an important element of Medea's character. She is intelligent and skilled in arts that exist on the border between medicine and sorcery. Had she been a man, she would have been a successful professional. However, she is a woman. That means that despite her intelligence, knowledge, skills, and brave and independent character, she is ultimately dependent on men, including her father, Jason, Creon, to a degree, and now Aegeus. Part of the anger and desire for revenge at the core of her character is a reaction to this sense of dependence, especially after her betrayal by Jason.
It is also worth noting that this scene emphasizes the plight of migrants. In the Athens of Euripides' own period, citizenship was restricted to those with Athenian grandparents. Immigrants could only be "metics" (a sort of resident alien). They lacked the rights of citizens and—unless they were very wealthy— they were forced to live a somewhat marginal existence despite often being skilled craftspeople. Thus, this scene reflects the precarious position of the immigrant and foreigner in the face of xenophobia and how such migrants live uncertain lives, dependent on the whims of rulers.

The appearance of Aegeus represents a crucial turning point in the play. By offering Medea sanctuary, he gives her the security and the confidence necessary to exact her terrible vengeance upon Jason. No longer is Medea now simply a wronged woman; she is an active, scheming aggressor with an insatiable thirst for revenge. As revenge is the main theme of the play, Aegeus's appearance is significant because it facilitates the implementation of Medea's wicked plan.
That plan, of course, includes the murder of her own children. And the scene with Aegeus has further significance in this regard. Aegeus agrees to provide Medea with sanctuary in return for magic drugs that will enhance his fertility. So, in other words, Aegeus's desire to have children provides Medea with the opportunity to kill hers. The arrival of Aegeus's future offspring sounds the death knell for Medea's children. There is a clear conflict here, one that reflects the significance of children in the overall story. Unwittingly, children are the source of much of the play's conflict. Aegeus desperately wants them; Medea desperately wants to get rid of hers.
Though often criticized for being clumsily constructed and implausible from a plot standpoint, there is no doubt that the scene with Aegeus contributes enormously to the play's dynamism, as well as carrying immense thematic importance in its own right.