The opening scene of Oedipus Rex is Oedipus standing before the people of Thebes, asking why are they are mourning. Speaking on behalf of the people, a priest explains to Oedipus that they (the people) are suffering - from famine, hunger, death, and sorrow. Oedipus decrees (in front of everyone) that he helped them once (speaking of solving the riddle of the sphynx) so certainly he will help them again. He promises to do whatever it takes to find the source of all this strife, and then eliminate it.
The significance of this is that this is the very scene where Oedipus dooms himself. First, he brags about how great and powerful he is as their king (his tragic flaw: hubris). Then, he promises to seek out the source of the problem (which turns out to be himself) and promises to get rid of it (which means he must learn that his fate to kill his father and marry his mother has come true and then eliminate himself from the kingdom - through banishment or death). This scene sets the tone of dramatic irony immediately. We, the audience, know the doom that awaits this powerful king. Oedipus is unaware of all of this. He does not even know of the fate spoken over him as a child, let alone that it came true even when his parents attempted to prevent it. Now, all we must do is watch (or read on) to witness what we know is inevitable destruction. What a hook!