What are Theseus and Hippolyta discussing at the play's start?
Theseus is the Duke of Athens. Hippolyta is the woman he is going to marry. They are going to be married quite soon (4 more days) and that is what they are talking about when the play starts.
Specifically, the two of them are talking about how eager they are to get married. They are really impatient for the four days to pass so that they can get married.
They only talk about this for a very little while in the first scene of the play. Very soon, they are interrupted by Egeus, who has come to have Theseus lay down the law to Egeus's daughter, Hermia.
Shakespeare's "A Midsummer Night's Dream" opens in the palace of the Greek Duke Theseus just four days before Theseus' marriage to Hippolyta:
Theseus is very impatient and complains that he has to wait for four more days before he can marry Hippolyta. She in turn advises him to be patient and assures him that these four days will quickly pass and then they can be happily married:
Theseus then orders his steward to go out into the streets of Athens and organise the festivities connected with his impending marriage: