In The Brothers by Terence, what is happening in this scene?

In this scene, Micio is attempting to inspire certain actions from his adopted son, Aeschinus; he's hoping that Aeschinus will admit to his relationship with Pamphila and be transparent about his motives in seeking out the young woman.

Just prior to the scene, we see Aeschinus lamenting the delicacy of his situation. Although he has been faithful to Pamphila (who has borne his child), rumor has it that he is having an affair with the music-girl he has carried off from Sannio's home. Aeschinus, being a faithful brother, does not want to tarnish his brother, Ctesipho's good name. However, Ctesipho is the one who is in love with the music-girl, and Aeschinus has just abducted her for Ctesipho' sake. Meanwhile, Aeschinus thinks to approach Pamphila and her mother, Sostrata, to explain the truth of the matter. He laments his own weakness at keeping his predicament a secret from his father, Micio, and thinks that he has lost his best chance to marry Pamphila.

As Aeschinus knocks on the door of Pamphila's home, out comes Micio, his father. Apparently, Micio has been apprised of the truth just recently and has been explaining the whole situation to Pamphila and Sostrata. However, Micio pretends that he doesn't know anything when Aeschinus bumps into him at the front door of Pamphila's home.

This is where your conversation comes in. Micio pretends that he is at Pamphila's home to represent the interests of a particular suitor for Pamphila's hand. He tells Aeschinus how impoverished the women are and that he has a friend who is Pamphila's next of kin. Micio slyly tells Aeschinus that this near relative of Pamphila's is interested in marrying her. Aeschinus responds, as an aside, that he is 'undone.' At this point, Aeschinus feels as if his future has been compromised and that his best chance for marrying the woman he loves has been lost.

Seeing his discomposure, Micio asks Aeschinus whether anything is the matter. You can see that Micio is trying to draw Aeschinus out, but the young man isn't ready to confess everything yet. So, Micio resorts to a masterful touch: he tells Aeschinus that this eager suitor is planning to take Pamphila back to his own home in Miletus. Aeschinus is dumbfounded and outwardly indignant when he hears this. Micio just replies that 'such is the act,' meaning that this is the state of affairs or that this is what's going to happen.

Micio goes on to say that the women don't have much choice since some unnamed rascal impregnated Pamphila without recognizing his obligations to Pamphila and the child. Aeschinus counters Micio's reasoning by drawing his father's attention to the feelings of the first suitor (in this case, he is referring to himself). He says that no one seems to have considered the feelings of the first man. Furthermore, he questions how anyone can expect a young woman like Pamphila to not fall in love until some relative comes to claim her for his wife. Sorely distressed, Aeschinus soon breaks down into tears.

Seeing this, Micio kindly explains that he knows everything. He admonishes his son to consider his actions in the light of having 'debauched a virgin' and to fulfill his responsibilities in such a circumstance. He also scolds Aeschinus for his lack of courage and his negligence; he says that Aeschinus' ambivalence has put the lives of Pamphila and his child in limbo for the last ten months. After scolding his son for keeping the matter from him, Micio gives Aeschinus permission to make good on his promise to Pamphila and to marry her.