In Oedipus Rex, what clue does Jocasta give to Oedipus concerning the central problem of the play?
We need to remember the central dramatic irony that runs throughout this play. Oedipus is trying to find out who has killed the former king of Thebes, Laius, and by so doing has brought down the plague upon Thebes which is killing its citizens. However, having pledged himself to discovering the murderer, Oedipus finds more and more clues to suggest that it was actually him who killed Laius, his father, and then married his mother.
In the part of the play you are referring to, Jocasta tells her husband/son that an oracle told Laius that he would be killed by his own son. Jocasta then says that Laius had his son abandoned to die on a lonely mountainside, so therefore, Laius could not have been killed by his son. Instead Laius was killed "By marauding strangers where three highways meet". It is this precise description of the manner and location of Laius's death that forces Oedipus to remember something that greatly disturbs him. Note how he responds to Jocasta:
How strange a shadowy memory crossed my mind,
Just now while you were speaking; it chilled my heart.
Oedipus doesn't fully remember yet, but as the play progresses and he assembles more and more clues, he discovers that the prophecy was fulfilled - it was he who killed his father and is the cause of the punishment of Thebes for this unnatural act of patricide and then the act of marrying his mother.