The setting of Oedipus Rex is one of tragedy. The city of Thebes is suffering from a horrible plague and people are in great pain. In this context, their leader, Oedipus is trying to solve this problem and bring comfort but it is to no avail. From this perspective, we can say that the situation is also very tense.
In this context, Tiresias is important, because he is the wise seer that knows what is going on and more importantly he knows why it is going on. The irony of the situation is that Tiresias is blind. The blind seer has supernatural insight. What makes this situation even more pronounced is that Oedipus is physically able to see perfectly, but when it comes to deeper matters like his identity he is really the one who is blind.
In a confrontation between Tiresias and Oedipus, Tiresias tells Oedipus point blank that he is the murderer that he is looking for. In a word, Oedipus is responsible for the plague of Thebes. In time, Oedipus is able to see this truth.